MultiAircraft Routing and Traffic Flow Management under Uncertainty


 Carmel Carson
 2 years ago
 Views:
Transcription
1 MultiAircraft Routing and Traffic Flow Management under Uncertainty Arnab Nilim Laurent El Ghaoui Vu Duong Abstract 1 Introduction A major ortion of the delay in the Air Traffic Management Systems (ATMS) in US and Euroe arises from the convective weather. In the current ractice of managing air traffic, the redicted storm zones are considered as deterministic obstacles and hence they are comletely avoided. As a result, the current strategy is too conservative and incurs a high delay. In reality, the dynamics of the convective weather is stochastic in nature. Hence, the caacity of the airsace is robabilistic, which reduces drastically with the convective weather. Our research objective is to deal with the dynamic and stochastic nature of the storms and add recourse in the routing and the flow management roblem. We address the multiaircraft flow management roblem using a stochastic dynamic rogramming algorithm, where the evolution of the weather is modelled as a stationary Markov chain. Our solution rovides a dynamic routing strategy for Naircraft that minimizes the exected delay of the overall system while taking into consideration of the constraints obtained by the sector caacities, as well as avoidance of conflicts among the aircraft. Our simulation suggests that a significant imrovement in delay can be obtained by using our methods over the existing methods. Research suorted in art by Eurocontrol , and DARPAF C Deartment of Electrical Engineering and Comuter Sciences, University of California, Berkeley. Internet: Deartment of Electrical Engineering and Comuter Sciences, University of California, Berkeley. Internet: Euro Control Exerimental Centre, BP BrtignysurOrge, Cedex, France. Internet: The air traffic management systems in US and Euroe are aroaching a critical saturation level. There has been a steady increase in delays over the last decade. Regular disrutions such as weather cause an exlosion of flight delays and cancellations. In figure 1, we see that the number of delayed flights due to convective weather has been increasing since the year 1995 [5]. There is a significant number of delayed flights all year long, with articularly high number of delays in the summer months. The airsace caacity reduces drastically with the resence of convective weather. The drastic reduction of airsace caacity interruts traffic flows and causes delays that rile through the system. Consequently, weather related delays contribute to around 80% of the total year in most of the years in US since Though the years 2001 and 2002 have been better (in terms of delays ) than the year 2000 due to weaker economy, the situation is exected to get worse in the coming years. Moreover, these delays do not deict the entire icture of the situation, as cancelled flights are not included in the figures. According to FAA, the cancellations have increased by 67% since The cost of delays to airlines and assengers are billions of US dollars er year. According to FAA 2002, the main sources that contribute to the delays in the US are weather, equiment, volume, and runways. Delays caused by weather are dynamic and stochastic in nature. Other sources cause delays which can be modelled in a deterministic framework. There has been a major effort to address delay in the traffic flow management roblem in the deterministic setting [1, 4, 8, 3, 6, 7, 9], where demand and caacities are considered deterministic. In these works, various traffic flow management algorithms are roosed 1
2 in order to reduce the system delay, given that the system caacity is exactly known. However, the major contributor of delay is weather, which is robabilistic in nature and cannot be addressed in this framework. In the National Airsace System, Federal Aviation Administration controllers and airline disatchers make Traffic flow management (TFM) and routing decisions 34 hours in advance of the actual oeration. Knowledge of the location and the intensity of the hazardous convective weather 34 hours ahead is key to select air routes. The rerouting and the redistribution strategies of the traffic affected by convective weather is discussed in recent works [5, 13]. The main focuss of these works has been to manage the traffic flow, given that the convective weather has already been taken lace in the airsace. In addition to these models, it is imerative to have a strategy where recourse is included in the lanning rocess, such that we can lan to relan under the weather uncertainty. In our revious work [11], we incororated recourse in the lanning rocess where we addressed the single aircraft roblem using Markov decision rocesses (where the weather rocesses is modelled as a stationary Markov chain) and a dynamic rogramming algorithm. Our aroach rovides a set of otimal decisions to a single aircraft that starts moving towards the destination along a certain ath, with the recourse otion of choosing a new ath whenever new information is obtained, such that the exected delay is minimized. As we addressed the roblem in the stochastic framework, we obtain the best olicy. In addition, we roosed an algorithm for dynamic routing where the solution is robust with resect to the estimation errors of the storm robabilities [10]. To the Bellman equations, which are derived in solving the dynamic routing strategy of an aircraft, we add a further requirements: we assume that the transition robabilities are unknown, but bounded within a convex set. Our algorithm otimizes the erformance of the system, given there are errors in the estimation of the robabilities of the storms. Figure 1: Number of total delayed flights vs delayed flights due to weather(in thousands) by year. Source: FAA OPSNET data. However, as the algorithms rovide a routing strategy for a single aircraft, they cannot solve a real life flow management roblem entirely which requires handling of multile aircraft. Moreover, the model that we used to describe the dynamics of the weather was exressed in a binary manner, where for each redicted zone, we allowed the convective weather to either stay or not stay. This is rather simlistic and cannot cature the real life dynamic nature of the weather. In this aer, we extend our model for multile aircraft. The roblem of routing under convective weather becomes much more comlex in a congested airsace because both aircraft conflicts and traffic flow management issues must be resolved at the same time. In this work, we rovide a dynamic routing strategy for multile aircraft that minimizes the exected delay of the overall system while satisfying the consideration of the constraints obtained by the sector caacity, as well as avoidance of conflicts among the aircraft. Moreover, we have used a more general weather dynamic model where the redicted zones can have more than two different states. 2 Weather uncertainty model Various weather teams (CCFP, ITWS etc) roduce redictions that some zones in the airsace may be unusable in certain time interval and their redictions are dynamically udated at every T = 15 minutes. The later an event is from the rediction time, the more unreliable it becomes. It is reasonable to assume that we have a deterministic knowledge of the weather in the time interval of 0 15 minutes in future. Hence, each aircraft has a erfect knowledge about the weather in the regions that are 15 minutes (15 times the velocity of the 2
3 aircraft rovides the distance) away from it. In this aer, we roose that each redicted convective weather zone can have multile outcomes. Deending on the coverage area and the We discritize time as 1, 2,..., n stages according to the weather udate. Stage 1 corresonds intensity of the rediction, we allow to have different realizations. Hence, the Markov chain that we to 0 15 minutes from the current time, stage 2 corresonds to minutes from the current roose is not a two state one, instead it is a l state time. We choose n that accommodates the worst Markov chain, where l is the number of ossible case routing of the aircraft. Let there is only one outcomes of the rediction in the region K 1 (figure storm that is redicted to take lace at the region 3). K 11, K 12,..., K 1l, are the ossible outcome regions K 1. In our revious work [11], we defined state in K 1 (K 1i K 1 i < l and K il = K 1 ). 0 1 corresonding to the state of having a storm in a region at a articular stage and state 0 corresonding to the state of having no storm at a corresonds to the state where there is no storm in the region k 1, 1 corresonds to the state where there is a storm, but only materialized in the region articular stage in that region. As we know the K 11, and so on. State l corresonds to the status of any storm in the time interval of 0 15 worst ossible outcome when K il or the whole region K 1 has been affected by the storm. We define minutes (stage 1), we can assign 0(1) deterministically to every storm at the stage 1. Moreover, PSfrag relacements ij as 11 the robability of the storm state to be j we assumed that we knew the conditional robability of having (not having) a storm in a region are in the 21 next stage if the current state is i. If there m 12 redicted convective zones, the system can in a 15 minutes time interval (stage q), given there be reresented 22 by a state of m tule vector, with a is a storm(no storm) in the revious stage (stage cardinality 23 of (l + 1) m. q 1) in the region, and the dynamics is considered Markovian. The conditional robability only l,l kl deends on the status of the storm in the stage l 1,l only. ll l ll 1 2 l lk However, this model cannot cature the realistic weather dynamics accurately. In figure 2, we see that the redicted convective weather vs actual weather in a tyical summer day. There are different colors associated with different redicted zones which corresond to different density, i.e., the ercentage of the area of the redicted zones that will be affected by the storm. The actual outcomes of the redictions are more comlex than that to be described by binary states. Instead of fully realizing in the worst form or not realizing at all, it can realize in many intermediate forms. Figure 3: A 2D view of the roblem. 3 Problem Formulation We consider a two dimensional flight lan of multile aircraft whose nominal aths are obstructed by redicted convective weathers. All the aircraft considered here are in the TMA/Enroute ortion of their flights. Hence, the velocities of all the aircraft considered are constant. Figure 2: A CCFP weather rediction vs actual weather in a summer day (19th May, 2001). We use a rectangular gridding system to reresent the airsace where we consider each grid oint as a way oint. If any aircraft is at a oint A at the beginning of the stage, and the solution of the roblem rovides the grid oint B that the aircraft will reach at the end of the stage, the aircraft will fly a straight line ath connecting A 3
4 and B. There are N aircraft currently ositioned at O 1, O 2,..., O N and the destination oints of the aircraft are D 1, D 2,..., D N (Figure 4). O i = [O i (x), O i (y)] T R 2, where O i (x) and O i (y) are resectively the x and y coordinates of the origin of aircraft i. Similarly, D i = [D i (x), D i (y)] T R 2, where D i (x) and D i (y) are resectively the x and y coordinates of the destination of aircraft i. Without the resence of convective weather, aircraft will try to follow the straight line connecting the origin and the destination, if those aths don t result in conflicts. There is a rediction that there can be m storms located at K 1,..., K m laces such that those zones might be unusable at certain time. w W are the weather states and W = (l + 1) m. The airsace that is considered here is confined in f sectors, and the caacities of the sectors are C 1,..., C f. The redictions are dynamically udated with time. In the current ractice, these stochastic convective zones are assumed to be comletely unusable, and solution roceeds as if they are deterministic constraints. As those zones were just redicted to be of unusable with a certain robability, it often turns out that the zones were erfectly usable. As the routing strategies do not use these resources, airsace resources are underutilized, leading to congestion in the remaining airsace through rile PSfrag relacements effect Origin O 2 O 1 O N weather Destination (redicted) D N D 2 D Figure 4: A 2D view of the roblem. In our roosed model, we will not exclude the zones which are redicted to be unusable (with some robability) at a certain time and we will take into consideration the fact that there will more udates with the course of flight and recourse will be alied accordingly. We take a less conservative route in avoiding the bad weather zone where we take a risk in delay to attain a better exected delay instead of avoiding the bad weather zones deterministically. We consider the following two schemes, 1. All of the N aircraft has the equal riority. 2. Every aircraft has different riority. Without the loss of generality, we assume that (riority of aircraft 1)>(riority of aircraft 2)>... >(riority of aircraft N). Scheme 1: All of the N aircraft has the equal riority. At each stage (15 minutes time san, before the next udate), the storm state is assumed to stay constant. X 1 R 2, X 2 R 2,..., X N R 2 reresent the locations of aircraft. If the state of the convective weather is w (as section 2), we define a state of the system as s = (w, X 1,..., X N ) R 2N+1, which reresents the ositions of all the aircraft and the storm situation. Furthermore, we define S as the set of all ossible states s. At any stage t, we want to choose an action (the directions of all the N aircraft to follow) from the set of allowable actions in state s, A s. Let, A = s S A s. We assume that S and A do not vary with time. If we decide to choose an action (the directions of all the N aircraft to follow) a A s in state s at the stage t, we ay a cost c t (s, a), which is the sum of distances travelled by N aircraft with the action a. For notational simlicity, we assume that the velocities of all the aircraft are equal (v AC ). Hence, if we minimize the exected distance travelled, we are minimize the exected delay. (Exactly the same otimization formulation holds even if the velocities of the aircraft are different from each other: where we need to multily the cost functions with aroriate multilying factors). Furthermore, we define an indicator function I kj (X k ), whose value is 1 if X k is in the sector j, and 0 otherwise. In our otimization roblem, we will like to minimize the exected sum of the distances travelled by N aircraft, while resolving all the otential conflicts and satisfying the sector caacity constraints. The otimization roblem can be written as, 4
5 min a A E s ( nt t=t c t (s, a) ) s.t. X i (t, w) X j i (t, w) 2 > r, i, j t w, I kj C j 0 j f, k where r is the minimum ermissible searation distance between two aircraft, and. 2 is the euclidian norm 1. Scheme 2: (riority of aircraft 1)>(riority of aircraft 2)>... >(riority of aircraft N) This is a sequential otimization roblem and the stes are as follows, Ste 1: In this ste, we assume that there is only one aircraft in the airsace and that is aircraft 1, which has the highest riority. The state of the otimization roblem is defined as s 1 = (w, X 1 ) S 1, where w is the storm state and X 1 is the osition of the aircraft 1. If we decide to choose an action a 1 A s1 in state s 1 at the stage t, we ay a cost c 1 t (s 1, a 1 ), which is the distance travelled by aircraft 1 with the action a 1. We otimize the following roblem, ) min a 1 A s1 E s1 ( nt t=t c 1 t (s 1, a 1 ) If we solve this otimization roblem, we obtain the otimal olicy a o 1 which rovides us X1 ot(t, w), the otimal osition of aircraft 1 at time t and the storm state w. Ste 2: In this ste, we only consider aircraft 2, which has the second highest riority. The state of the otimization roblem s 2 = (w, X 2 ) S 2. At any stage t, we want to choose an action (the direction aircraft 2 to follow) from the set of allowable actions in state s 2, A s2. Let, A 2 = s2 S 2 A s2. For the aircraft 2, we solve the following otimization roblem, ) min a 2 A s2 E s2 ( nt t=t c 2 t (s 2, a 2 ) X 2 (t, w) X 1 ot(t, w) 2 > r, 0 t nt w, 1 If M = (M 1, M 2,..., M ) R, then M 2 = M M 2. and obtain X 2 ot(t, w). Ste 3 Ste N: We kee following the same rocedure till we have solved for all N aircraft. For the N th aircraft,which has the lowest riority, the otimization roblem is the following, min a N A sn E sn ( nt t=t c N t (s N, a N ) s.t. X N (t, w) X 1 ot(t, w) 2 > r, t w, X N (t, w) X 2 ot(t, w) 2 > r, t w,... X N (t, w) X (N 1) ot (t, w) 2 > r, t w, I kj C j 0 j f, k where Xot, 1..., X (N 1) ot iterations. ) are obtained from revious In both of the schemes, we look for the best olicy. Determining the best olicy is to decide where to go next given the currently available information. We consider the set of decisions facing all of the aircraft that start moving towards the destination along a certain ath, with the recourse otion of choosing a new ath whenever a new information is obtained. 4 Markov Decision Process Finitestate and finiteaction Markov Decision Processes (MDPs) cature several attractive features that are imortant in decisionmaking under uncertainty: they handle risk in sequential decisionmaking via a state transition robability matrix, while taking into account the ossibility of information gathering and recourse corresonding to this information during the multistage decision rocess [12, 2]. The Markov decision rocess has the finite state X, and the finite action set A. We denote by P = (P a ) a A the collection of transition matrices, and by c t (i, a) the cost corresonding to state i and action a at time t, and denote by c T the cost function at the terminal time, T. The otimization roblem is to minimize the 5
6 exected cost over a finite horizon: ( T 1 ) min E c t (i t, a t ) + c T (i T ) a A t=0 where a = (a 0,..., a T 1 ) denotes the strategy and A the strategy sace. When the transition matrices are known, the value function can be comuted via the Bellman recursion V t (i) = min a A c t (i, a) + j P a (i, j)v t+1 (j). 5 Solution of Traffic Flow Management where all of the N aircraft has the equal riority (scheme 1) We roose a Markov Decision Process algorithm to solve the traffic flow management where each of the N aircraft has same riority. The stes of the algorithm are as follows, Ste 1: Preliminary calculations The state of the Markov Decision Process (MDP) for this roblem is s = (w, X 1, X 2,..., X N ) ((2N + 1) tule vector) and s S (defined in the section 3). If we discritize the airsace by D number of nodes, S = D 2N (l+1) m. There are n stages in this MDP (obtained in section 2). In addition, we need to calculate the action set of the MDP. Actions of this MDP are the directions of all the N aircraft to follow in each stage with different realizations of the weather. We can obtain the action a, that is the directions of the aircraft to follow if we calculate the oints that can be reached by each aircraft in the next 15 minutes, given their current ositions. This can be aroximately calculated if we draw an annular region with 15 v AC ± ɛ as radii, with a redefined angle θ and checking which grid oints fall in the region. Once we have the set of all ossible controls, we readily obtain P a from the weather data. Ste 2: Assigning aroriate costs We assign costs in such a way that our algorithm rovides aths that include going through the zones in the absence of storms while avoid it if there is a storm. Furthermore, it should also make sure that there is no conflict among N aircraft. We define c(w, X 1,..., X N, (X 1i ),..., (X Ni )) as the sum of all 1 k N costs obtained by aircraft k to go to X Ki from X k. Provision 1: Avoid if storm, otherwise take a shortcut We introduce a function P ROV 1 : R 4N+1 {0, 1} in order to rovide us the rovision of avoiding a zone if there is a storm, otherwise taking a shortcut. If 1 k N, (X ki {k 1 ork 2 or..k m }) or ({the line segment (λx ki + (1 λ)x k and 0 λ 1 ) connecting the oints X k, X ki cut any of the redicted storm zone } & { the storm state w corresonds to a storm at that articular zone}) P ROV 1 (w, X 1,..., X N, X 1i,..., X Ni ) = 1, P ROV 1 (w, X 1,..., X N, X 1i,..., X Ni ) = 0 Provision 2: Avoid conflict among each other First, we introduce a function CF v1 v 2 : R 2 R 2 R 2 R 2 {0, 1}, where it takes the origin and destination oints of two aircraft with velocities v 1 and v 2 and rovides 1 if they are in conflict and 0 otherwise. We will demonstrate how to obtain CF v1 v 2 (I 1, F 1, I 2, F 2 ), where I j is the initial oint and F j is the final oint of the aircraft j. At time t, the ositions of aircraft 1 and 2 are I 1 + F 1 I 1 F 1 I 1 2 v 1 t and I 2 + F 2 I 2 F 2 I 2 2 v 2 t resectively. The distance between them at time t, d(t) = I ( W )t 2, where U 1 = F 1 I 1 F 1 I 1 2, U 1 = F 2 I 2 F 2 I 2 2, I = I 2 I 1, and W = (v 1 U 1 v 2 U 2 ). arg min t d(t) = arg min t ( I t W ) T ( I t W ). In order to find the otimal time t at which two aircraft come to the closest oint, we set t ( I W t) T ( I W t) = 0. Solving this, we obtain t = W T I W T W. If t < 0, the two aircraft are diverging, hence CF v1 v 2 (I 1, F 1, I 2, F 2 ) = 0. Also, if I + t W 2 > r, CF v1 v 2 (I 1, F 1, I 2, F 2 ) = 0, CF v1 v 2 (I 1, F 1, I 2, F 2 ) = 1. In this roblem, as we have assumed that all the aircraft are flying at the same seed, we can write CF (,.,.,.,.) instead of CF v1 v 2 (,.,.,.,.). In addition, we introduce a function P ROV 2 : R 4N {0, 1} that rovides us the rovision of conflict avoidance. 6
7 If l, k, X li X ki 2 > r & CF (X l, X li, X k, X ki ) = 0, P ROV 2 (X 1,..., X N, X 1i,..., X Ni ) = 0, P ROV 2 (X 1,..., X N, X 1i,..., X Ni ) = 1 Finally, the cost function is defined as following, if P ROV 1 (w, X 1,..., X N, X 1i,..., X Ni ) P ROV 2 (X 1,..., X N, X 1i,..., X Ni ) = 1, c(w, X 1,..., X N, X 1i,..., X Ni ) =, = 1 & c(w, X 1,..., X N, X 1i,..., X Ni ) = N k=1 Xki X k 2 Assigning aroriate Value func Ste 3: tion We define V t (s) as the value function which is the exected minimum distance to go if the current state is s and the current stage is t. We need to add the following rovisions in the value function in order to obtain the correct solution. Provision 1: Reach the destination oints The value function should have boundary conditions such that we obtain a comlete ath (ath stating at the origin and ending at the destination) as a solution. For the destination oints D 1,..., D N, the conditions below would guarantee that the solution will rovide a comlete ath. For any state weather state w and the last stage n, if {X 1 = D 1 },..., {X 1 = D 1 } V n (w, X 1,..., X N ) = 0, V n (w, X 1,..., X N ) = Provision 2: Direct cost at the end of the flight We assign the boundary values to the value function for the states which corresonds to the aircraft locations that are less than 15v AC aart from the destination oints. Let the state corresonds to the aircraft location of X 1,..., X N and ( (X i D i 2 15v AC i) and the stage t > 1. If (w corresonds to the storm state such that no storm zone intersects the straight line {λx k + (1 λ)d k and 0 λ 1} ) V t (w, X 1,..., X N ) = k Xk D k 2, for any t > 1, V t (w, X 1,..., X N ) = Provision 3: Sector Caacity In order to ensure that the total number of aircraft in a sector at any time does not exceed the sector caacity, we assign value function aroriately. For a state s = (w, X 1,..., X N ), if there exists at least one j such that k I kj > Cj, then V t =. Imlementing the recursive equa Ste 4: tions The recursive equation that solves the roblem is as follows, V t (s) = min a A {c(s, a) + s P a (s, s )V t+1 (s )}. We use the backward dynamic rogramming technique to solve these equations. We start with the final stage and go back iteratively to the first stage and obtain solutions for every stage and for every state. At the first stage, the solution is readily obtained as we know the current state. The aircraft will kee continue flying according to the solution till a new udate is obtained. At the next stage, we will receive a new udate, which corresonds to a new state. As we have already calculated all the otimal control for all ossible states, we just check the vector V 2 (.) and obtain the control. The aircraft will roceed in this way till they reach the destination oints (checking the vector V n (.)). In this way, we comute a routing strategy that rovides the minimum exected delay. 6 Solution of Traffic Flow Management with different riority (scheme 2) In this scheme, we assume that (riority of aircraft 1)>(riority of aircraft 2)>... >(riority of aircraft N) (as described in the section 3). Ste 1: Otimal route for aircraft 1 In this ste, we find the otimal route for aircraft 1, which has the highest riority. In a sense, we assume that there is no aircraft in the airsace. 7
8 The MDP state s 1 = (w, X 1 ) R 3 and s 1 S 1 (defined in the section 3). We discritize the airsace and time in a same way as described in section 5 and section 2, which yields S 1 = D 2 (l + 1) m, and n stages in this MDP. Actions of this MDP are the directions of aircraft 1 to follow in each stage with different realizations of the weather. As described in section 5, we obtain the action a 1, that is the directions of aircraft 1 to follow if we calculate the oints that can be reached by aircraft 1 in the next 15 minutes, given its current osition. We define c 1 (w, X 1, X 1i ) as the cost to go if the aircraft 1 goes from X 1 to X 1i in a stage. For assigning the aroriate value, we only need to add rovision 1 (calculation of which is same as described in section 5: ste 2: rovision 1). As there is only one aircraft, there is no need to add the rovision for conflict avoidance. The value function for the MDP is defined as Vt 1 (s 1 ), which is the exected minimum distance to go if the current state is s 1 and the current stage is t. In the value function, we add the the first two rovisions (the calculation is same as described in section 5: ste 4: rovision 1and 2 ). As there is no other aircraft in the airsace, we do not need to add any rovision that require satisfying the sector caacities. Once we have assigned all the boundary values roerly, we can solve the following recursion, V 1 t (s 1 ) = min a 1 A 1 {c 1 (s 1, a 1 )+ s 1 P a (s 1, s 1)V 1 t+1(s 1)}, and we obtain the solution of the recursion which rovides us X 1 ot(t, w). Ste 2 N: Otimal route for aircraft 2 N We follow the same rocedure in the next stes, excet we add the rovisions that rohibit conflicts and satisfy the sector caacity constraints. In the the second ste, we add the conflict avoidance rovision in the cost function, where Xot(t, 1 w) t w are considered NOGO zones. We use the same rocedure described in section 5: ste 3: rovision 2, where we assign high cost for violating these constraints. In each iteration, we kee a record of I kj and assign a very a high value to the value function if the sector caacity constraints are violated. When we solve the aroriate recursion, these additional features will guarantee the conflict avoidance and satisfy the sector caacity constraints. For the N th aircraft, which has the lowest riority, the rovision 2 for cost function will be as follows, if 1 k N 1, X Ni X ki 2 > r & CF (X N, X Ni, Xot, k Xot) ki = 0, P ROV2 N(XN, X Ni ) = 0, P ROV2 N(XN, X Ni ) = 1 The cost function will be defined in the same way (section 5) using these two rovisions. Also, Vt N (.) is very high for the states which violates the sector caacity constraints. With this rovisions in the cost and value functions, we can solve the recursion and obtain otimal strategy for all of the N aircraft that minimize the delay, given the above riority scheme. This scheme avoids combinatorial exlosion as S 1 = S 2 =... = S N = D 2 (l + 1) m. On the other hand, as this is a more constrained otimization roblem, it yields higher delays than the scheme 1. 7 Various alications in the Euroean airsace In the Euroean airsace, weather is not as acute of a roblem as in US. However, the algorithms resented here can be alied to some imortant roblems that arise in Euroe as well. Routing under congested airsace: Stochastic obstacles that occur frequently in Euroe is the congested airsace. The dynamics of the congested airsace is stochastic in nature. The remaining caacity of the airsace to be used by the aircraft outside the congested airsace can be exressed in a Markovian model. Our roosed MDP algorithm can be readily alied to the roblem involving the caacity uncertainty due to congestion. Routing of latoon of aircraft under uncertainty: In Euroe, multile aircraft fly in a latoon to go to a same destination oint, where riorities are given according to the osition in the latoon; i.e., the leading aircraft getting the highest riority and the second in line getting the second highest riority and so on. We can aly our algorithm (scheme 2) in order to obtain the otimal routing strategy of the aircraft. The solution will also yield the diverging (when the aircraft get searated) and converging (when they merge again) 8
9 oints of the latoon. This is actually a secial case of the algorithm roosed by us where all the destination oints are same. 8 Simulation In this section, we discus the results of the imlementation of both of our algorithms in various scenarios involving dynamic routing and traffic flow management of multile aircraft under uncertainty. We have imlemented both of the algorithms in MATLAB and we ran our exeriment on a standard PC. In the first exeriment, there are two aircraft with origins at O 1 = [0, 96] T, and O 2 = [0, 96] T, and destinations at D 1 = [312, 96] T and D 2 = [312, 96] T (all the units in n.mi.). The velocities of the aircraft are 480 n.mi/hour. There is a rediction of a convective weather. The storm zone is a rectangle whose corner oints are [168, 96] T, [168, 96] T, [192, 96] T, [192, 96] T, which may obstruct the nominal flight ath of the aircraft. Moreover, there is a critical airsace within this zone which will definitely be affected if the the storm takes lace. The critical zone is assumed a rectangle with corner oints [168, 60] T, [168, 60] T, [192, 60] T, [192, 60] T (the shaded zone in figure 5). We assume that the weather information of the ortion of the airsace that can be reached in 15 minutes is deterministic and the robability of the storm roagates in a Markovian fashion with time. Also, the minimum searation distance between two aircraft, r = 5(n.mi) in this examle. The weather udate is received once every 15 minutes. We discritize the time in 15 minutes time intervals (stages). We define 0 as the state when there is no storm, 1 as the state when only the critical zone is affected by the storm, and 2 as the state when the whole redicted zone has been affected by the storm. The rediction matrix is a follows, P = P (i + 1, j + 1) corresonds to the robability that the storm state will be j in the next stage, if the current storm state is i; i.e., P (2, 1) = 0.3 means that the robability that the storm state will be 1 (no storm) in the next stage is 0.3 given the current storm state is 0 (only critical zone is affected by the storm). PSfrag relacements Weather O 1 (Predicted) D 2 O 2 D Figure 5: Routing of two aircraft. In this scenario, we imlemented both of our strategies (scheme 1 and 2) and comared their erformances with the traditional strategy (TS) where the convective zone is avoided as if it is a deterministic obstacle while avoiding conflicts. We define Delay Measure (DMi A ) as the extra flight ath required by aircraft i in a strategy A in excess of the nominal flight ath (which is the Euclidean distance between the origin and the destination; (n.mi.) in this roblem); DMij A = DMi A + DMj A. Furthermore, we introduce a erformance metric Imrovement Measure ) of Strategy A over B, which is the ercentage of the maximum ossible imrovement gained for aircraft i by using strategy A instead (IM A/B i of using strategy B ; IM A/B i = 100 DM B i DM A i DM B i and IM A/B ij = 100 DM ij B DM ij A. Higher IM corre DMij B sonds to better delay. In TS, if we resolve the conflict, aircraft 1 and 2 follow aths with a length of 2 = = n.mi). DM T S 1 = DM T S 88.78, and DM T S 12 = DM T S 1 + DM T S 2 = Using the scheme 1, where both aircraft have equal riority, aircraft 1 and 2 will initially follow a ath with an angle of and resectively till they get the next udate. Both of them will avoid the storm zone when there is a storm and take a direct route if there is no storm and the solution of the strategy is conflict free. In this way, both the aircraft follow a flight ath that yield a exected delay of (n.mi.).,
10 DM1 1 = DM 2 1 1/T S = 32.33, IM1 = IM 1/T S = IM 1/T S 12 = = 63.58%. Similarly PSfrag relacements O 1 O if we use scheme 2, where aircraft 1 has higher riority over the aircraft 2, aircraft 1 and 2 initially O 3 O fly at an angle and till they get the next udate. Similar to the scheme 1, both of them 150 will avoid the storm zone when there is a storm and D 2 D1 200 take a direct route if there is no storm and the solution of the strategy is conflict free. The exected distance travelled by the aircraft are (n.mi.) and (n.mi.) resectively; IM 2/T S Figure 6: Routing of three aircraft. 1 = 78.95%, IM 2/T S 2 = 40.18%, and IM 2/T S 12 = 56.76%. The summary of the result is resented in 1. is 58.35% (figure 7). IM of Scheme 1 over TS IM of Scheme 2 over TS Aircraft % % Aircraft % 40.18% System % 56.76% Platoon Destination Table 1: Imrovement comarisons PSfrag relacements We observe that we obtain a better system delay in case of scheme 1. However, in real life, deending uon the aircraft tye, size, and hub and soke network, it might be more reasonable to rioritize the routing strategy. Moreover, the comutation time for scheme 2 is 8.31 seconds, which is much faster than the comutation time for scheme 1 (7.46 minutes). We can avoid a combinatorial exlosion in case of scheme 2 and can handle large number of aircraft. There is no significant comutation cost in adding an extra aircraft. In order to illustrate this oint, if we add one more aircraft in the system with O 3 = [0, 0] T and D 3 = [360, 0] T (figure 6), our algorithm gives the routing strategy for aircraft 3 with an additional 4.84 secs. Aircraft 3 should have an initial angle of , which yields IM 2/T S 3 = 34.62% (for aircraft 3) and IM 2/T S 123 = 51.23% (for the system). In addition, we ran an exeriment for the same weather rediction where a latoon of aircraft are ositioned at O 1 = [48, 48] T, O 2 = [24, 24] T, and O 3 = [0, 0] T. The destination oint for all of the them is [360, 0 T ] and (riority of aircraft 1)>(riority of aircraft 2)>(riority of aircraft 3). Initial vector rovided by our algorithms for the aircraft are , , and The system level IM obtained by using scheme 2 over TS Figure 7: Routing of a latoon of aircraft. 9 Conclusion In this aer, we rovide a traffic flow management tool that can be used by Air Traffic Controller or Airline Disatcher to dynamically route multile aircraft under uncertain weather. Our solution rovides a routing strategy for aircraft which minimizes the exected delay of the system. Moreover, as it rovides less circuitous routes, it inhibits the overloading of aircraft in the neighboring sectors of the redicted storm zones. Consequently, it restricts the rile effect of delay due to convective weather. The comlexity of the comutation deends on the number of the aircraft, the origindestination air, size and location of the storms, tye of storm, level of discretization, and the rate of information udates. The comlexity of the algorithm, when all the aircraft have equal riority, does not scale well with the number of aircraft. However, when 10
11 each aircraft has different riorities, the algorithm is scalable; i.e., the algorithm scales olynomially with the number of aircraft. In real life, a mixed scheme is more aroriate; aircraft are rioritized in a number of sets such that aircraft in different sets have the different riorities, but the aircraft within each set have the same riority. Our algorithm can be readily alied to the mixed scheme. Currently, we are develoing a riority scheme based on the game theoretic model that will be fair to all the articiants in the system. In addition, we are working on roosing an aroximate dynamic rogramming model that can handle large scale roblems involving a large number of aircraft and convective zones. References [1] N. Barnier, P. Brisset, and T. Rivire. Slot allocation with constraint rogramming: Models and results. In Proc. of the Fourth International Air Traffic Management R&D Seminar ATM, Santa Fe, New Mexico, [2] D. Berstsekas and J. Tsitsiklis. Neuro Dynamic Programming. Athena Scientific, Massachusetts, [3] Dimitris Bertsimas and Sarah atterson. The air traffic flow management roblem with enroute caacities. Oerations Research, 26: , [4] K. Lindsey C. Burlingame, A. Boyd. Traffic flow management modeling with the time assignment model. Technical reort, The MITRE CORPORATION MP 93W , Virginia, [5] J. Evans. Tactical decision suort to comlement strategic traffic flow management for convective weather. In Proc. of the Fourth International Air Traffic Management R&D Seminar ATM, Santa Fe, New Mexico, [6] J. Goodhart. Increasing Aitline Oerational Control in a Constrained Air Traffic System. PhD thesis, Deartment of Industrial Engineering and Oerations Research, University of California, Berkeley, [7] B. Lucio. Multilevel aroach to atc roblems: Online strategy control of flights. International Journal of Systems Science, 21: , [8] B. Nicoletti M. Bielli, G. Calicchio and S. Riccardelli. The air traffic flow control roblem as an alication of network theory. Comutation and Oerations Research, 9: , [9] H. Marcia. The otential of network flow models for managing air traffic. Technical reort, The MITRE CORPORATION MP 93W , Virginia, [10] A. Nilim, L. El Ghaoui, and V. Duong. Robust dynamic routing of aircraft under uncertianty. In Proc. of the 21st Digital Avionics Systems Conference, Irvine, Califonia, [11] A. Nilim, L. El Ghaoui, V. Duong, and M. Hansen. Trajectorybased air traffic management (tbatm) under weather uncertainty. In Proc. of the Fourth International Air Traffic Management R&D Seminar ATM, Santa Fe, New Mexico, [12] M. Putterman. Markov Decision Processes: Discrete Stochastic Dynamic Programming. WileyInterscince, New York, [13] J. E. Sherry, C.G. Ball, and S.M. Zobell. Traffic flow management (tfm) weather rerouting. In Proc. of the Fourth International Air Traffic Management R&D Seminar ATM, Santa Fe, New Mexico, Author Biograhies Arnab Nilim is a Ph.D. student in the Deartment of Electrical Engineering and Comuter Sciences (EECS) at the University of California Berkeley. Laurent El Ghaoui is an Associate Professor in the Deartment of EECS at the University of California Berkeley. Vu Duong is the Head of Innovative Research at Euro Control Exerimental Center. Acknowledgment: The authors would like to thank Jim Evans, Mark Hansen and Pravin Varaiya for interesting discussions and comments. 11
Synopsys RURAL ELECTRICATION PLANNING SOFTWARE (LAPER) Rainer Fronius Marc Gratton Electricité de France Research and Development FRANCE
RURAL ELECTRICATION PLANNING SOFTWARE (LAPER) Rainer Fronius Marc Gratton Electricité de France Research and Develoment FRANCE Synosys There is no doubt left about the benefit of electrication and subsequently
More informationStatic and Dynamic Properties of Smallworld Connection Topologies Based on Transitstub Networks
Static and Dynamic Proerties of Smallworld Connection Toologies Based on Transitstub Networks Carlos Aguirre Fernando Corbacho Ramón Huerta Comuter Engineering Deartment, Universidad Autónoma de Madrid,
More informationA MOST PROBABLE POINTBASED METHOD FOR RELIABILITY ANALYSIS, SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION
9 th ASCE Secialty Conference on Probabilistic Mechanics and Structural Reliability PMC2004 Abstract A MOST PROBABLE POINTBASED METHOD FOR RELIABILITY ANALYSIS, SENSITIVITY ANALYSIS AND DESIGN OPTIMIZATION
More informationAn important observation in supply chain management, known as the bullwhip effect,
Quantifying the Bullwhi Effect in a Simle Suly Chain: The Imact of Forecasting, Lead Times, and Information Frank Chen Zvi Drezner Jennifer K. Ryan David SimchiLevi Decision Sciences Deartment, National
More informationLargeScale IP Traceback in HighSpeed Internet: Practical Techniques and Theoretical Foundation
LargeScale IP Traceback in HighSeed Internet: Practical Techniques and Theoretical Foundation Jun Li Minho Sung Jun (Jim) Xu College of Comuting Georgia Institute of Technology {junli,mhsung,jx}@cc.gatech.edu
More informationRisk in Revenue Management and Dynamic Pricing
OPERATIONS RESEARCH Vol. 56, No. 2, March Aril 2008,. 326 343 issn 0030364X eissn 15265463 08 5602 0326 informs doi 10.1287/ore.1070.0438 2008 INFORMS Risk in Revenue Management and Dynamic Pricing Yuri
More informationSQUARE GRID POINTS COVERAGED BY CONNECTED SOURCES WITH COVERAGE RADIUS OF ONE ON A TWODIMENSIONAL GRID
International Journal of Comuter Science & Information Technology (IJCSIT) Vol 6, No 4, August 014 SQUARE GRID POINTS COVERAGED BY CONNECTED SOURCES WITH COVERAGE RADIUS OF ONE ON A TWODIMENSIONAL GRID
More informationPoint Location. Preprocess a planar, polygonal subdivision for point location queries. p = (18, 11)
Point Location Prerocess a lanar, olygonal subdivision for oint location ueries. = (18, 11) Inut is a subdivision S of comlexity n, say, number of edges. uild a data structure on S so that for a uery oint
More informationService Network Design with Asset Management: Formulations and Comparative Analyzes
Service Network Design with Asset Management: Formulations and Comarative Analyzes Jardar Andersen Teodor Gabriel Crainic Marielle Christiansen October 2007 CIRRELT200740 Service Network Design with
More informationBuffer Capacity Allocation: A method to QoS support on MPLS networks**
Buffer Caacity Allocation: A method to QoS suort on MPLS networks** M. K. Huerta * J. J. Padilla X. Hesselbach ϒ R. Fabregat O. Ravelo Abstract This aer describes an otimized model to suort QoS by mean
More informationMachine Learning with Operational Costs
Journal of Machine Learning Research 14 (2013) 19892028 Submitted 12/11; Revised 8/12; Published 7/13 Machine Learning with Oerational Costs Theja Tulabandhula Deartment of Electrical Engineering and
More informationTitle: Stochastic models of resource allocation for services
Title: Stochastic models of resource allocation for services Author: Ralh Badinelli,Professor, Virginia Tech, Deartment of BIT (235), Virginia Tech, Blacksburg VA 2461, USA, ralhb@vt.edu Phone : (54) 2317688,
More informationThe Online Freezetag Problem
The Online Freezetag Problem Mikael Hammar, Bengt J. Nilsson, and Mia Persson Atus Technologies AB, IDEON, SE3 70 Lund, Sweden mikael.hammar@atus.com School of Technology and Society, Malmö University,
More informationA Simple Model of Pricing, Markups and Market. Power Under Demand Fluctuations
A Simle Model of Pricing, Markus and Market Power Under Demand Fluctuations Stanley S. Reynolds Deartment of Economics; University of Arizona; Tucson, AZ 85721 Bart J. Wilson Economic Science Laboratory;
More informationAn inventory control system for spare parts at a refinery: An empirical comparison of different reorder point methods
An inventory control system for sare arts at a refinery: An emirical comarison of different reorder oint methods Eric Porras a*, Rommert Dekker b a Instituto Tecnológico y de Estudios Sueriores de Monterrey,
More information1 Gambler s Ruin Problem
Coyright c 2009 by Karl Sigman 1 Gambler s Ruin Problem Let N 2 be an integer and let 1 i N 1. Consider a gambler who starts with an initial fortune of $i and then on each successive gamble either wins
More informationReDispatch Approach for Congestion Relief in Deregulated Power Systems
ReDisatch Aroach for Congestion Relief in Deregulated ower Systems Ch. Naga Raja Kumari #1, M. Anitha 2 #1, 2 Assistant rofessor, Det. of Electrical Engineering RVR & JC College of Engineering, Guntur522019,
More informationTworesource stochastic capacity planning employing a Bayesian methodology
Journal of the Oerational Research Society (23) 54, 1198 128 r 23 Oerational Research Society Ltd. All rights reserved. 165682/3 $25. www.algravejournals.com/jors Tworesource stochastic caacity lanning
More informationMultiperiod Portfolio Optimization with General Transaction Costs
Multieriod Portfolio Otimization with General Transaction Costs Victor DeMiguel Deartment of Management Science and Oerations, London Business School, London NW1 4SA, UK, avmiguel@london.edu Xiaoling Mei
More informationUniversiteitUtrecht. Department. of Mathematics. Optimal a priori error bounds for the. RayleighRitz method
UniversiteitUtrecht * Deartment of Mathematics Otimal a riori error bounds for the RayleighRitz method by Gerard L.G. Sleijen, Jaser van den Eshof, and Paul Smit Prerint nr. 1160 Setember, 2000 OPTIMAL
More informationA Virtual Machine Dynamic Migration Scheduling Model Based on MBFD Algorithm
International Journal of Comuter Theory and Engineering, Vol. 7, No. 4, August 2015 A Virtual Machine Dynamic Migration Scheduling Model Based on MBFD Algorithm Xin Lu and Zhuanzhuan Zhang Abstract This
More informationThe Optimal Sequenced Route Query
The Otimal Sequenced Route Query Mehdi Sharifzadeh, Mohammad Kolahdouzan, Cyrus Shahabi Comuter Science Deartment University of Southern California Los Angeles, CA 900890781 [sharifza, kolahdoz, shahabi]@usc.edu
More informationLoad Balancing Mechanism in Agentbased Grid
Communications on Advanced Comutational Science with Alications 2016 No. 1 (2016) 5762 Available online at www.isacs.com/cacsa Volume 2016, Issue 1, Year 2016 Article ID cacsa00042, 6 Pages doi:10.5899/2016/cacsa00042
More informationENFORCING SAFETY PROPERTIES IN WEB APPLICATIONS USING PETRI NETS
ENFORCING SAFETY PROPERTIES IN WEB APPLICATIONS USING PETRI NETS Liviu Grigore Comuter Science Deartment University of Illinois at Chicago Chicago, IL, 60607 lgrigore@cs.uic.edu Ugo Buy Comuter Science
More informationAn Efficient Method for Improving Backfill Job Scheduling Algorithm in Cluster Computing Systems
The International ournal of Soft Comuting and Software Engineering [SCSE], Vol., No., Secial Issue: The Proceeding of International Conference on Soft Comuting and Software Engineering 0 [SCSE ], San Francisco
More informationWeb Application Scalability: A ModelBased Approach
Coyright 24, Software Engineering Research and Performance Engineering Services. All rights reserved. Web Alication Scalability: A ModelBased Aroach Lloyd G. Williams, Ph.D. Software Engineering Research
More informationMultiChannel Opportunistic Routing in MultiHop Wireless Networks
MultiChannel Oortunistic Routing in MultiHo Wireless Networks ANATOLIJ ZUBOW, MATHIAS KURTH and JENSPETER REDLICH Humboldt University Berlin Unter den Linden 6, D99 Berlin, Germany (zubow kurth jr)@informatik.huberlin.de
More informationDesign of A Knowledge Based Trouble Call System with Colored Petri Net Models
2005 IEEE/PES Transmission and Distribution Conference & Exhibition: Asia and Pacific Dalian, China Design of A Knowledge Based Trouble Call System with Colored Petri Net Models HuiJen Chuang, ChiaHung
More informationCOST CALCULATION IN COMPLEX TRANSPORT SYSTEMS
OST ALULATION IN OMLEX TRANSORT SYSTEMS Zoltán BOKOR 1 Introduction Determining the real oeration and service costs is essential if transort systems are to be lanned and controlled effectively. ost information
More informationCBus Voltage Calculation
D E S I G N E R N O T E S CBus Voltage Calculation Designer note number: 3121256 Designer: Darren Snodgrass Contact Person: Darren Snodgrass Aroved: Date: Synosis: The guidelines used by installers
More informationService Network Design with Asset Management: Formulations and Comparative Analyzes
Service Network Design with Asset Management: Formulations and Comarative Analyzes Jardar Andersen Teodor Gabriel Crainic Marielle Christiansen October 2007 CIRRELT200740 Service Network Design with
More informationMonitoring Frequency of Change By Li Qin
Monitoring Frequency of Change By Li Qin Abstract Control charts are widely used in rocess monitoring roblems. This aer gives a brief review of control charts for monitoring a roortion and some initial
More informationConcurrent Program Synthesis Based on Supervisory Control
010 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 30July 0, 010 ThB07.5 Concurrent Program Synthesis Based on Suervisory Control Marian V. Iordache and Panos J. Antsaklis Abstract
More informationFinding a Needle in a Haystack: Pinpointing Significant BGP Routing Changes in an IP Network
Finding a Needle in a Haystack: Pinointing Significant BGP Routing Changes in an IP Network Jian Wu, Zhuoqing Morley Mao University of Michigan Jennifer Rexford Princeton University Jia Wang AT&T Labs
More informationThe fast Fourier transform method for the valuation of European style options inthemoney (ITM), atthemoney (ATM) and outofthemoney (OTM)
Comutational and Alied Mathematics Journal 15; 1(1: 16 Published online January, 15 (htt://www.aascit.org/ournal/cam he fast Fourier transform method for the valuation of Euroean style otions inthemoney
More informationAdaptive Routing Using a Virtual Waiting Time Technique
76 EEE TRANSACTONS ON SOFTWARE ENGNEERNG, VOL. SE8, NO. 1, JANUARY 1982 Adative Routing Using a Virtual Waiting Time Technique ASHOK K. AGRAWALA, SENOR MEMBER, EEE, SATSH K. TRPATH, AND GLENN RCART, MEMBER,
More informationSTATISTICAL CHARACTERIZATION OF THE RAILROAD SATELLITE CHANNEL AT KUBAND
STATISTICAL CHARACTERIZATION OF THE RAILROAD SATELLITE CHANNEL AT KUBAND Giorgio Sciascia *, Sandro Scalise *, Harald Ernst * and Rodolfo Mura + * DLR (German Aerosace Centre) Institute for Communications
More informationDAYAHEAD ELECTRICITY PRICE FORECASTING BASED ON TIME SERIES MODELS: A COMPARISON
DAYAHEAD ELECTRICITY PRICE FORECASTING BASED ON TIME SERIES MODELS: A COMPARISON Rosario Esínola, Javier Contreras, Francisco J. Nogales and Antonio J. Conejo E.T.S. de Ingenieros Industriales, Universidad
More informationMemory management. Chapter 4: Memory Management. Memory hierarchy. In an ideal world. Basic memory management. Fixed partitions: multiple programs
Memory management Chater : Memory Management Part : Mechanisms for Managing Memory asic management Swaing Virtual Page relacement algorithms Modeling age relacement algorithms Design issues for aging systems
More informationOn Software Piracy when Piracy is Costly
Deartment of Economics Working aer No. 0309 htt://nt.fas.nus.edu.sg/ecs/ub/w/w0309.df n Software iracy when iracy is Costly Sougata oddar August 003 Abstract: The ervasiveness of the illegal coying of
More informationDiscrete Stochastic Approximation with Application to Resource Allocation
Discrete Stochastic Aroximation with Alication to Resource Allocation Stacy D. Hill An otimization roblem involves fi nding the best value of an obective function or fi gure of merit the value that otimizes
More informationComparing Dissimilarity Measures for Symbolic Data Analysis
Comaring Dissimilarity Measures for Symbolic Data Analysis Donato MALERBA, Floriana ESPOSITO, Vincenzo GIOVIALE and Valentina TAMMA Diartimento di Informatica, University of Bari Via Orabona 4 76 Bari,
More informationBranchandPrice for Service Network Design with Asset Management Constraints
BranchandPrice for Servicee Network Design with Asset Management Constraints Jardar Andersen Roar Grønhaug Mariellee Christiansen Teodor Gabriel Crainic December 2007 CIRRELT200755 BranchandPrice
More informationTimeCost TradeOffs in ResourceConstraint Project Scheduling Problems with Overlapping Modes
TimeCost TradeOffs in ResourceConstraint Proect Scheduling Problems with Overlaing Modes François Berthaut Robert Pellerin Nathalie Perrier Adnène Hai February 2011 CIRRELT201110 Bureaux de Montréal
More informationComputational Finance The Martingale Measure and Pricing of Derivatives
1 The Martingale Measure 1 Comutational Finance The Martingale Measure and Pricing of Derivatives 1 The Martingale Measure The Martingale measure or the Risk Neutral robabilities are a fundamental concet
More informationCRITICAL AVIATION INFRASTRUCTURES VULNERABILITY ASSESSMENT TO TERRORIST THREATS
Review of the Air Force Academy No (23) 203 CRITICAL AVIATION INFRASTRUCTURES VULNERABILITY ASSESSMENT TO TERRORIST THREATS Cătălin CIOACĂ Henri Coandă Air Force Academy, Braşov, Romania Abstract: The
More informationA Study of Active Queue Management for Congestion Control
In IEEE INFOCOM 2 A Study of Active Queue Management for Congestion Control Victor Firoiu Marty Borden 1 vfiroiu@nortelnetworks.com mborden@tollbridgetech.com Nortel Networks TollBridge Technologies 6
More informationOn the (in)effectiveness of Probabilistic Marking for IP Traceback under DDoS Attacks
On the (in)effectiveness of Probabilistic Maring for IP Tracebac under DDoS Attacs Vamsi Paruchuri, Aran Durresi 2, and Ra Jain 3 University of Central Aransas, 2 Louisiana State University, 3 Washington
More informationOn the predictive content of the PPI on CPI inflation: the case of Mexico
On the redictive content of the PPI on inflation: the case of Mexico José Sidaoui, Carlos Caistrán, Daniel Chiquiar and Manuel RamosFrancia 1 1. Introduction It would be natural to exect that shocks to
More informationIntroduction to NPCompleteness Written and copyright c by Jie Wang 1
91.502 Foundations of Comuter Science 1 Introduction to Written and coyright c by Jie Wang 1 We use timebounded (deterministic and nondeterministic) Turing machines to study comutational comlexity of
More informationMigration to Object Oriented Platforms: A State Transformation Approach
Migration to Object Oriented Platforms: A State Transformation Aroach Ying Zou, Kostas Kontogiannis Det. of Electrical & Comuter Engineering University of Waterloo Waterloo, ON, N2L 3G1, Canada {yzou,
More informationLocal Connectivity Tests to Identify Wormholes in Wireless Networks
Local Connectivity Tests to Identify Wormholes in Wireless Networks Xiaomeng Ban Comuter Science Stony Brook University xban@cs.sunysb.edu Rik Sarkar Comuter Science Freie Universität Berlin sarkar@inf.fuberlin.de
More informationCharacterizing and Modeling Network Traffic Variability
Characterizing and Modeling etwork Traffic Variability Sarat Pothuri, David W. Petr, Sohel Khan Information and Telecommunication Technology Center Electrical Engineering and Comuter Science Deartment,
More informationOn Multicast Capacity and Delay in Cognitive Radio Mobile Adhoc Networks
On Multicast Caacity and Delay in Cognitive Radio Mobile Adhoc Networks Jinbei Zhang, Yixuan Li, Zhuotao Liu, Fan Wu, Feng Yang, Xinbing Wang Det of Electronic Engineering Det of Comuter Science and Engineering
More informationAn effective multiobjective approach to prioritisation of sewer pipe inspection
An effective multiobjective aroach to rioritisation of sewer ie insection L. Berardi 1 *, O.Giustolisi 1, D.A. Savic 2 and Z. Kaelan 2 1 Technical University of Bari, Civil and Environmental Engineering
More informationIEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 2011 757. LoadBalancing Spectrum Decision for Cognitive Radio Networks
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 29, NO. 4, APRIL 20 757 LoadBalancing Sectrum Decision for Cognitive Radio Networks LiChun Wang, Fellow, IEEE, ChungWei Wang, Student Member, IEEE,
More information4 Perceptron Learning Rule
Percetron Learning Rule Objectives Objectives  Theory and Examles  Learning Rules  Percetron Architecture 3 SingleNeuron Percetron 5 MultileNeuron Percetron 8 Percetron Learning Rule 8 Test Problem
More informationThis document is downloaded from DRNTU, Nanyang Technological University Library, Singapore.
This document is downloaded from DRNTU, Nanyang Technological University Library, Singaore. Title Automatic Robot Taing: AutoPath Planning and Maniulation Author(s) Citation Yuan, Qilong; Lembono, Teguh
More informationOptimal Routing and Scheduling in Transportation: Using Genetic Algorithm to Solve Difficult Optimization Problems
By Partha Chakroborty Brics "The roblem of designing a good or efficient route set (or route network) for a transit system is a difficult otimization roblem which does not lend itself readily to mathematical
More informationRisk and Return. Sample chapter. e r t u i o p a s d f CHAPTER CONTENTS LEARNING OBJECTIVES. Chapter 7
Chater 7 Risk and Return LEARNING OBJECTIVES After studying this chater you should be able to: e r t u i o a s d f understand how return and risk are defined and measured understand the concet of risk
More informationThe Economics of the Cloud: Price Competition and Congestion
Submitted to Oerations Research manuscrit The Economics of the Cloud: Price Cometition and Congestion Jonatha Anselmi Basque Center for Alied Mathematics, jonatha.anselmi@gmail.com Danilo Ardagna Di. di
More informationSimulink Implementation of a CDMA Smart Antenna System
Simulink Imlementation of a CDMA Smart Antenna System MOSTAFA HEFNAWI Deartment of Electrical and Comuter Engineering Royal Military College of Canada Kingston, Ontario, K7K 7B4 CANADA Abstract:  The
More informationProject Management and. Scheduling CHAPTER CONTENTS
6 Proect Management and Scheduling HAPTER ONTENTS 6.1 Introduction 6.2 Planning the Proect 6.3 Executing the Proect 6.7.1 Monitor 6.7.2 ontrol 6.7.3 losing 6.4 Proect Scheduling 6.5 ritical Path Method
More informationDrinking water systems are vulnerable to
34 UNIVERSITIES COUNCIL ON WATER RESOURCES ISSUE 129 PAGES 344 OCTOBER 24 Use of Systems Analysis to Assess and Minimize Water Security Risks James Uber Regan Murray and Robert Janke U. S. Environmental
More informationAutomatic Search for Correlated Alarms
Automatic Search for Correlated Alarms KlausDieter Tuchs, Peter Tondl, Markus Radimirsch, Klaus Jobmann Institut für Allgemeine Nachrichtentechnik, Universität Hannover Aelstraße 9a, 0167 Hanover, Germany
More informationThe Priority RTree: A Practically Efficient and WorstCase Optimal RTree
The Priority RTree: A Practically Efficient and WorstCase Otimal RTree Lars Arge Deartment of Comuter Science Duke University, ox 90129 Durham, NC 277080129 USA large@cs.duke.edu Mark de erg Deartment
More informationF inding the optimal, or valuemaximizing, capital
Estimating RiskAdjusted Costs of Financial Distress by Heitor Almeida, University of Illinois at UrbanaChamaign, and Thomas Philion, New York University 1 F inding the otimal, or valuemaximizing, caital
More informationCABRS CELLULAR AUTOMATON BASED MRI BRAIN SEGMENTATION
XI Conference "Medical Informatics & Technologies"  2006 Rafał Henryk KARTASZYŃSKI *, Paweł MIKOŁAJCZAK ** MRI brain segmentation, CT tissue segmentation, Cellular Automaton, image rocessing, medical
More informationAn Associative Memory Readout in ESN for Neural Action Potential Detection
g An Associative Memory Readout in ESN for Neural Action Potential Detection Nicolas J. Dedual, Mustafa C. Ozturk, Justin C. Sanchez and José C. Princie Abstract This aer describes how Echo State Networks
More informationPressure Drop in Air Piping Systems Series of Technical White Papers from Ohio Medical Corporation
Pressure Dro in Air Piing Systems Series of Technical White Paers from Ohio Medical Cororation Ohio Medical Cororation Lakeside Drive Gurnee, IL 600 Phone: (800) 4480770 Fax: (847) 855604 info@ohiomedical.com
More informationAn Introduction to Risk Parity Hossein Kazemi
An Introduction to Risk Parity Hossein Kazemi In the aftermath of the financial crisis, investors and asset allocators have started the usual ritual of rethinking the way they aroached asset allocation
More informationA Brief Overview of Intermodal Transportation
A Brief Overview of Intermodal Transortation Tolga Bektas Teodor Gabriel Crainic January 2007 CIRRELT200703 Tolga Bektas 1, Teodor Gabriel Crainic 1,* 1 Interuniversity Research Centre on Enterrise Networks,
More informationVariations on the Gambler s Ruin Problem
Variations on the Gambler s Ruin Problem Mat Willmott December 6, 2002 Abstract. This aer covers the history and solution to the Gambler s Ruin Problem, and then exlores the odds for each layer to win
More informationModeling and Simulation of an Incremental Encoder Used in Electrical Drives
10 th International Symosium of Hungarian Researchers on Comutational Intelligence and Informatics Modeling and Simulation of an Incremental Encoder Used in Electrical Drives János Jób Incze, Csaba Szabó,
More informationFDA CFR PART 11 ELECTRONIC RECORDS, ELECTRONIC SIGNATURES
Document: MRM1004GAPCFR11 (0005) Page: 1 / 18 FDA CFR PART 11 ELECTRONIC RECORDS, ELECTRONIC SIGNATURES AUDIT TRAIL ECO # Version Change Descrition MATRIX 449 A Ga Analysis after adding controlled documents
More informationStochastic Derivation of an Integral Equation for Probability Generating Functions
Journal of Informatics and Mathematical Sciences Volume 5 (2013), Number 3,. 157 163 RGN Publications htt://www.rgnublications.com Stochastic Derivation of an Integral Equation for Probability Generating
More informationFluent Software Training TRN99003. Solver Settings. Fluent Inc. 2/23/01
Solver Settings E1 Using the Solver Setting Solver Parameters Convergence Definition Monitoring Stability Accelerating Convergence Accuracy Grid Indeendence Adation Aendix: Background Finite Volume Method
More informationIEEM 101: Inventory control
IEEM 101: Inventory control Outline of this series of lectures: 1. Definition of inventory. Examles of where inventory can imrove things in a system 3. Deterministic Inventory Models 3.1. Continuous review:
More informationAsymmetric Information, Transaction Cost, and. Externalities in Competitive Insurance Markets *
Asymmetric Information, Transaction Cost, and Externalities in Cometitive Insurance Markets * Jerry W. iu Deartment of Finance, University of Notre Dame, Notre Dame, IN 465565646 wliu@nd.edu Mark J. Browne
More informationMinimizing the Communication Cost for Continuous Skyline Maintenance
Minimizing the Communication Cost for Continuous Skyline Maintenance Zhenjie Zhang, Reynold Cheng, Dimitris Paadias, Anthony K.H. Tung School of Comuting National University of Singaore {zhenjie,atung}@com.nus.edu.sg
More informationEvaluating a WebBased Information System for Managing Master of Science Summer Projects
Evaluating a WebBased Information System for Managing Master of Science Summer Projects Till Rebenich University of Southamton tr08r@ecs.soton.ac.uk Andrew M. Gravell University of Southamton amg@ecs.soton.ac.uk
More informationMicroscopic Simulation of Pedestrian Flows
Hoogendoorn 1 Microscoic Simulation of Pedestrian Flows Serge P. Hoogendoorn (s.hoogendoorn@ct.tudelft.nl) Transortation and Traffic Engineering Section Faculty of Civil Engineering and Geosciences Delft
More informationHigh Quality Offset Printing An Evolutionary Approach
High Quality Offset Printing An Evolutionary Aroach Ralf Joost Institute of Alied Microelectronics and omuter Engineering University of Rostock Rostock, 18051, Germany +49 381 498 7272 ralf.joost@unirostock.de
More informationPiracy and Network Externality An Analysis for the Monopolized Software Industry
Piracy and Network Externality An Analysis for the Monoolized Software Industry Ming Chung Chang Deartment of Economics and Graduate Institute of Industrial Economics mcchang@mgt.ncu.edu.tw Chiu Fen Lin
More informationLarge firms and heterogeneity: the structure of trade and industry under oligopoly
Large firms and heterogeneity: the structure of trade and industry under oligooly Eddy Bekkers University of Linz Joseh Francois University of Linz & CEPR (London) ABSTRACT: We develo a model of trade
More informationAn optimal batch size for a JIT manufacturing system
Comuters & Industrial Engineering 4 (00) 17±136 www.elsevier.com/locate/dsw n otimal batch size for a JIT manufacturing system Lutfar R. Khan a, *, Ruhul. Sarker b a School of Communications and Informatics,
More informationX How to Schedule a Cascade in an Arbitrary Graph
X How to Schedule a Cascade in an Arbitrary Grah Flavio Chierichetti, Cornell University Jon Kleinberg, Cornell University Alessandro Panconesi, Saienza University When individuals in a social network
More informationThe risk of using the Q heterogeneity estimator for software engineering experiments
Dieste, O., Fernández, E., GarcíaMartínez, R., Juristo, N. 11. The risk of using the Q heterogeneity estimator for software engineering exeriments. The risk of using the Q heterogeneity estimator for
More informationJoint Production and Financing Decisions: Modeling and Analysis
Joint Production and Financing Decisions: Modeling and Analysis Xiaodong Xu John R. Birge Deartment of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208,
More informationOPTIMAL EXCHANGE BETTING STRATEGY FOR WINDRAWLOSS MARKETS
OPTIA EXCHANGE ETTING STRATEGY FOR WINDRAWOSS ARKETS Darren O Shaughnessy a,b a Ranking Software, elbourne b Corresonding author: darren@rankingsoftware.com Abstract Since the etfair betting exchange
More informationStorage Basics Architecting the Storage Supplemental Handout
Storage Basics Architecting the Storage Sulemental Handout INTRODUCTION With digital data growing at an exonential rate it has become a requirement for the modern business to store data and analyze it
More informationA Novel Architecture Style: Diffused Cloud for Virtual Computing Lab
A Novel Architecture Style: Diffused Cloud for Virtual Comuting Lab Deven N. Shah Professor Terna College of Engg. & Technology Nerul, Mumbai Suhada Bhingarar Assistant Professor MIT College of Engg. Paud
More informationCompensating Fund Managers for RiskAdjusted Performance
Comensating Fund Managers for RiskAdjusted Performance Thomas S. Coleman Æquilibrium Investments, Ltd. Laurence B. Siegel The Ford Foundation Journal of Alternative Investments Winter 1999 In contrast
More informationNEWSVENDOR PROBLEM WITH PRICING: PROPERTIES, ALGORITHMS, AND SIMULATION
Proceedings of the 2005 Winter Simulation Conference M. E. Kuhl, N. M. Steiger, F. B. rmstrong, and J.. Joines, eds. NEWSVENDOR PROBLEM WITH PRICING: PROPERTIES, LGORITHMS, ND SIMULTION Roger L. Zhan ISE
More informationFREQUENCIES OF SUCCESSIVE PAIRS OF PRIME RESIDUES
FREQUENCIES OF SUCCESSIVE PAIRS OF PRIME RESIDUES AVNER ASH, LAURA BELTIS, ROBERT GROSS, AND WARREN SINNOTT Abstract. We consider statistical roerties of the sequence of ordered airs obtained by taking
More informationWeb Inv. Web Invoicing & Electronic Payments. What s Inside. Strategic Impact of AP Automation. Inefficiencies in Current State
Pay tream A D V I S O R S WHITE PAPER Web Inv Web Invoicing Strategic Imact of AP Automation What s Inside Inefficiencies in Current State Key Drivers for Automation Web Invoicing Comonents New Automation
More informationManaging specific risk in property portfolios
Managing secific risk in roerty ortfolios Andrew Baum, PhD University of Reading, UK Peter Struemell OPC, London, UK Contact author: Andrew Baum Deartment of Real Estate and Planning University of Reading
More informationFailure Behavior Analysis for Reliable Distributed Embedded Systems
Failure Behavior Analysis for Reliable Distributed Embedded Systems Mario Tra, Bernd Schürmann, Torsten Tetteroo {tra schuerma tetteroo}@informatik.unikl.de Deartment of Comuter Science, University of
More informationComputing the Most Probable String with a Probabilistic Finite State Machine
Comuting the Most Probable String with a Probabilistic Finite State Machine Colin de la Higuera Université de Nantes, CNRS, LINA, UMR6241, F44000, France cdlh@univnantesfr Jose Oncina De de Lenguajes
More informationA Multivariate Statistical Analysis of Stock Trends. Abstract
A Multivariate Statistical Analysis of Stock Trends Aril Kerby Alma College Alma, MI James Lawrence Miami University Oxford, OH Abstract Is there a method to redict the stock market? What factors determine
More information