Probabilistic Offload Scheme in Integrated Cellular WiFi Systems

Transcription

1 Probabilistic Offload Scheme in Integrated Cellular WiFi Systems Insook Kim and Dongwoo Kim The Department of Electronic and Communication Engineering Hanyang University, Ansan, South Korea {kimins, Abstract WiFi offloading is a cost-effective way of alleviating the problem of highly congested cellular networks. In this paper, we consider WiFi offloading problem in an integrated cellular WiFi system consisting of mobile base station (MBS and WiFi access point (AP. We propose a probabilistic offloading scheme, cellular packets that arrive at the queue of MBS are offloaded to the queue of WiFi AP with an offload probability. The offload probability is determined to minimize the average delay experienced by the cellular packets while guaranteeing stability of both cellular and WiFi system. We model the arrivals and fulfillments of data services of a cellular operator as an M/M/ queue. We investigate two priority disciplines: First-In-First-Out (FIFO and Non-Preemptive Priority Rule (NPPR. We provide an exact optimal offload probability for FIFO, but present an upper bound on the optimal probability for NPPR. Numerical investigation is used to verify the optimality of the proposed solutions, to examine the effect of packet arrival rate of MBS and compare the average delays for FIFO and NPPR. Index Terms WiFi offloading; delay; stability; queueing. I. INTRODUCTION Cellular networks worldwide have been facing an unprecedented growth in mobile data traffic. According to Cisco s forecast, mobile data traffic will increase by -fold between 23 and 28 globally []. The network capacity is growing at a much slower pace, and cannot keep up with the explosive growth in data traffic [2]. As a cost-effective way of alleviating the problem of highly congested mobile networks, WiFi offloading has attracted a lot of attention recently due to its advantages: lower cost, higher data rates, lower ownership cost, etc. Cellular operators rely heavily on WiFi offloading: currently about half of all cellular data traffic is proactively offloaded through unlicensed spectrum [3]. The literature for the study of the mobile data offloading is extensive [4]-[] (and references therein. Previous works on WiFi offloading mainly aim to reduce the traffic load in the cellular network or cellular data plan consumption by offloading as much data traffic through the WiFi network as possible. For the mobile users (MUs in a congested area with a WiFi coverage, such data offloadng schemes may result in a congested WiFi network, and thus This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF funded by the Ministry of Education, Science and Technology (NRF- 23RAA2679 and the Second-Phase Brain Korea 2 Plus Project in 24. a poor quality of service for the users. In [2], the authors considered the congestion-aware network selection problem considering the network congestion, switching penalty, and network pricing in data offloading. In this paper, we consider the stability of WiFi system to determine how much to offload data traffic to WiFi. A queueing model has been advocated as a framework to study the performance of mobile data offloading [9]-[]. In [9], they proposed a queueing analytic model that can be used to understand the performance improvements achievable by WiFi-based data offloading, as a function of WiFi availability and performance, and user mobility and traffic load. In [], the authors developed an analytical framework using an embedded Markov process for the delayed offloading system, if there is currently no WiFi availability, (some traffic can be delayed up to some chosen time threshold, instead of being sent immediately over the cellular interface. In [], they presented a queueing analysis of offloading performance in a vehicular environment. In this paper, we propose a probabilistic offloading scheme, data traffic originally targeted towards the cellular network is offloaded to WiFi networks with an offload probability. The offload probability is constrained by the stability of the system. Stability is defined as the state all the queues in the system are stable. There are several works using the stability as the performance criterion of interest [2]-[4]. Also, we characterize the performance of the proposed offloading scheme by the average delay. The average delay is defined as the average time spent in the system by a packet, which includes the waiting time in a queue until transmitted and the transmission time. We model the arrivals and fulfillments of data services of a cellular operator as an M/M/ queue. To determine the offload probability, we formulate an optimization problem to minimize the average delay while guaranteeing the stability of the system. We investigate two priority disciplines: First-In-First-Out (FIFO and Non-Preemptive Priority Rule (NPPR, which are discussed in detail later. For FIFO, an exact optimal offload probability is provided, but an upper bound on the optimal probability is presented for NPPR. The rest of the paper is organized as follows. We describe our system model and formulate an optimization problem to determine the optimal offload probability in Section II. We

2 λ m λ w (-pλ m offloading pλ m Fig.. System model. MBS AP present an exact optimal offload probability for FIFO and an upper bound on the optimal probability for NPPR in Section III. We provide numerical results in Section IV, and finally conclude in Section V µ m µ w II. SYSTEM MODEL AND PROBLEM FORMULATION We assume a simple wireless network consisting of one mobile base station (MBS and one small-scale operator, specifically, WiFi access point (AP. Each transmitter (MBS and AP has a buffer of infinite capacity to store incoming packets. The packets arrive at MBS and AP according to a Poisson process with rate λ m and λ w, respectively. We assume that the time duration need to successfully transmit a packet of cellular network is exponentially distributed with a finite mean /µ m. Similarly, a packet is successfully transmitted via WiFi network with exponentially distributed time of /µ w. We call this time duration service time. It depends on the channel condition of the link between a transmitter and a receiver and packet length. Thus average departure rates of packets in each queue are µ m and µ w, respectively. The assumptions above allow MBS and AP to be modeled as an M/M/ queuing system. We assume that λ m > λ w and µ m < µ w. It means that the queue of MBS is more busy than that that of AP. A packet arriving a highly congested system may wait for a long time until being served (transmitted successfully. To alleviate congestion of the queue, MBS can offload a part of packets from its cellular traffic to WiFi AP. In this paper, we propose an offload scheme a packet arriving at the queue of MBS can be offloaded to WiFi AP with probability p. We call p offload probability and the scheme the probabilistic offload scheme. The offload probability should be determined so as to guarantee the stability of each system. A queue is said to be stable if and only if the probability of being empty remains nonzero for time t that grows to infinity [2] lim P [Q(t ] > ( t Q(t denotes the unfinished work (in packets of the queue at time t. The stability of the system can be checked by using Loynes theorem [5]. This states that the queue is stable, if the average arrival rate λ is less than the average departure rate µ, then the queue is stable; on the other hand, if the average arrival rate λ is greater than the average departure rate µ, the queue is unstable; finally, if λ µ, the queue can be either stable or unstable [2]. In the proposed probabilistic offload scheme, the packet arrival at queue of MBS is decomposed into two streams: with rate ( pλ m to MBS and with rate pλ m to AP. Meanwhile, two Poisson streams of packets are arrived at the queue of AP, with rate λ w and pλ m. A Poisson stream can be de decomposed into any number of mutually independent component Poisson processes and the superposition of n streams of Poisson arrivals is again a Poisson stream with mean equal to the sum of the means of the component streams [6]. Thus, the packet arrivals resulted from traffic offloading are still Poisson process with rate ( pλ m and λ w pλ m at the queues of MBS and AP, respectively. We define the effective arrival rates of queues of MBS and AP as the adjusted arrival rates by traffic offloading. Let λ m,e and λ w,e denote the effective arrival rates of queues of MBS and WiFi AP, respectively. λ m,e ( pλ m and λ w,e λ w pλ m. (2 To guarantee the stability of each queue, the offload probability should satisfy the following conditions: λ m,e < µ m and λ w,e < µ w. (3 From (3, we find the range of p that makes the both systems to be stable. p min p p max, (4 { p min max µ } { } m µw λ w, and p max min,. λ m λ m (5 The equal signs in (4 are used for mathematical tractability. We define average delay as the average time spent in the system by a packet, which includes the waiting time in a queue until transmitted and the transmission time. Let W m and W w denote delay of cellular system and WiFi, respectively. A packet originated from the cellular network expects delay of W m with probability p and W w with probability p. Thus the average delay of a cellular packet is given by W ( pw m pw w. (6 We aim to minimize the average delay of a cellular packet while guaranteeing the stability of each system. The problem we have is (P min p W ( pw m pw w (7 s.t. p min p p max. (8 The exact forms of W m and W w can be determined depending on service scheduling types: a normal or priority queue, which are discussed in detail in the next section.

3 III. THE OPTIMAL OFFLOAD PROBABILITY In this section, we present an optimal offload probability by solving the optimization problem (P. We consider two priority disciplines: First-In-First-Out (FIFO and Non-Preemptive Priority Rule (NPPR. A. Normal queue : FIFO A queue in each system has a normal queue. All packets are transmitted in order of arrival, i.e., first-in-first-out (FIFO. In this case, W m and W w can be written as [7] W m, (9 µ m ( pλ m W w Thus the objective function of (P is W FIFO µ w (λ w pλ m. ( p p. ( µ m ( pλ m µ w λ w pλ m It can be easily shown that 2 W FIFO > over p 2 min p p max. Therefore the optimization problem has an optimal solution over p min p p max. Proposition : The optimal offload probability is given by p min, p < p min, p, p min p p max, (2 p max, p max < p, p λ m µm (µ w λ w (µ m λ m µ w λ w µm µ w λ w. (3 Proof: The first derivation of W FIFO with respect to p is W FIFO µ m (µ m λ m pλ m 2 µ w λ w (µ w λ w pλ m 2. (4 Equating (4 to zero, we can calculate p as given in (3. Since p might be beyond the range of [p min, p max ], we arrive at the optimal offload probability as given in (2 depending on the value of p. B. Priority queue : NPPR In this section, we assume that WiFi AP is able to tell packets offloaded from MBS with its own packets (originated WiFi system and gives a priority to its own packets. Remind that, with an offload probability of p, WiFi packets and offloaded packets arrive according to independent Poisson processes with rate λ w and pλ m, respectively. The service time (transmission time of all packets are exponentially distributed with the same means /µ w. We assume that WiFi packets are treated with priority over offloaded packets. We consider Non-Preemptive Priority Rule (NPPR. WiFi packets can move ahead of all the offloaded packets waiting in the queue, but an offloaded packet in service is not interrupted by WiFi packets. That is, when an offloaded packet is in service and a WiFi packet arrives, the WiFi packet waits until the service (transmission of the offloaded packet has been completed. For an M/M/ system with the non-preemptive priority rule, the average delay of an offloaded packet can be expressed by [7] W w (o µ2 w λ w (µ w λ w pλ m µ w (µ w λ w (µ w λ w pλ m. (5 The superscript (o represents an offloaded packet. Notice that the average delay of a WiFi packet having high-priority is different from (5. Since the queue of MBS has only the packets from the cellular network, W m is equivalent to in (9 regardless of the service priority rule. Thus the objective function of (P is expressed by W NPPR p µ m ( pλ m p ( µ 2 w λ w (µ w λ w pλ m µ w (µ w λ w (µ w λ w pλ m. (6 The first and second derivatives of the objective function W NPPR are obtained by, respectively W NPPR µ m (µ w λ m pλ m 2 µ w (µ w λ w pλ m 2 λ w. (7 (µ w λ w µ w 2 W NPPR 2λ m µ m 2 (µ w λ m pλ m 3 2λ m µ w (µ w λ w pλ m 3. (8 The second derivative of the objective function in (8 is still positive over the range of [p min, p max ]. A zero of (7, denoted by p, can be an optimal solution if it exists in [p min, p max ]. It is difficult to obtain the closed-form of p. However, the numerical solution can be obtained by using the root-finding algorithms such as Bisection method and Newton s method [8]. The optimal offload probability to WiFi with priority queue can be written as NP P R p min, p < p min, p, p min p p max, p max, p max < p, (9 Although we do not have an exact closed form of p, we intuitively would expect that NP P R popt because an offloaded packet in the priority-wifi queue waits longer than in nonpriority-wifi queue. Proposition 2 states this: Proposition 2: The optimal probability of offload to the prioritized WiFi system, NP P R is less than or equal to popt in (2, i.e. NP P R popt. Proof: See Appendix. IV. NUMERICAL RESULTS We provide the numerical results on the proposed probabilistic offload scheme and investigate its performance in this section. We use µ m and µ w.5. When an offloaded packet is in service and a WiFi packet arrives, the service (transmission of the offloaded packet can be interrupted, which is called preemptive priority rule.

4 Average delay (W Optimal average delay (W opt normal queue (λ w priority queue (λ w normal queue (λ w.5 priority queue (λ w.5 normal queue (λ w.2 priority queue (λ w.2 2 W W m W w Offload probability (p Packet arrival rate of MBS (λ m Fig. 2. Average delay with respect to offload probability. (λ m.4, µ m, λ w, and µ w.5. Fig. 4. Average delay per packet with optimal offload probability. (µ m, µ w.5. Optimal offload probability ( normal queue (λ w.3 priority queue (λ w normal queue (λ w.5 priority queue (λ w.5.25 normal queue (λ w.2 priority queue (λ w Packet arrival rate of MBS (λ m Fig. 3. Optimal offload probability. (µ m, µ w.5. In Fig. 2, we plot the curve of average delay with respect to p for FIFO to verify that the presented solution in Proposition is optimal. We use λ m.4 and λ w. Notice that λ m /µ m > and thus a queue of MBS is unstable without traffic offloading (or other solution to resolve network congestion. The queue of MBS becomes stable by offloading traffic of MBS to WiFi AP. The delay at queue of MBS (the red dashed curve decreases while the delay at queue of WiFi AP (the blue dotted curve increases as the value of an offload probability increases. We can see that the average delay for the normal queue (the black solid curve has the minimum at p.53273, which is equivalent to the value obtained by (2. Fig. 3 and 4 depict the optimal offload probability and the minimum average delay of a cellular packet with respect to λ m for λ w.2,.5 and, respectively. The solid and the dotted lines represent the normal queue case (section III-A and the priority queue case (section III-B, respectively. The lines in Fig. 3 and 4 break at λ m.9 and.45 when λ w.5 and, respectively. This is because both systems are not stable beyond these points. In Fig. 3, it is observed that is monotonically decreasing as λ m increases for λ w.2 while increasing for λ w. Meanwhile, keeps unchanged for λ m.5. It can be shown that the slope of depends on the sign of µ m µ w λ w by differentiating with respect to λ m. opt λ m µm µw λ w ( µm µ w λ w ( µm µ w λ w (2 In this example, µ m µ w λ w for λ w.5, so the value of (2 becomes zero and is constant. Fig. 3 shows that the optimal offload probability of the priority queue case is lower than that of normal queue case. It coincides with the conclusion in Proposition 2. Fig. 4 depicts the minimum average delays of a cellular packet for FIFO (normal queue and NPPR (priority queue, respectively. For both cases, the average delay increases as the packet arrival rates increases. The average delay increases gradually and then rapidly when λ m(w,e /µ m(w,e is close to unity. Fig. 4 shows that WiFi packets high priority over offloaded packets increases the average delays of cellular packets. The gap of the average delay between normal and priority queue significantly increases when the packet arrival rate at WiFi AP is high. V. CONCLUSION λ 2 m In this paper, we have considered one MBS wants to offload its cellular traffic to WiFi AP. We have proposed a probabilistic offloading scheme. The packet which arrives at the queue of MBS is offloaded to the queue of WiFi AP with offload.

5 probability p. The offload probability p is determined to minimize the average delay experienced by cellular packets while guaranteeing stability of both systems (cellular and WiFi. We have provided an exact optimal offload probability for FIFO, but present an upper bound on the optimal probability for NPPR. It is shown that WiFi packets high priority over offloaded packets increases the average delays of cellular packets. In the future work, we will consider the more general case with service time and finite queue capacity. APPENDIX PROOF OF PROPOSITION 2 First, we show that p > p. Remind that p and p are roots of WFIFO and WNPPR, respectively. We can express the equations as f(p and W FIFO f(p g(p, W NPPR f(p g(p h(p, µ m (µ w λ m pλ m 2, g(p µ w λ w (µ w λ w pλ m 2, h(p (2 λ w (µ w λ w pλ m 2 λ w (µ w λ w µ w. (22 Obviously, f(p is monotonously decreasing with respect to p while g(p and h(p are monotonously increasing. p is a point the graphs of y f(p and y g(p intersect. And the graphs of y f(p and y g(p h(p intersect at p p. Since h(p is positive over [p min, p max ], the graph of y g(p h(p moves upward as shown in Fig. 5. Thus, p is at the left side of p, i.e., p > p. Now, we consider three cases depending on the value of p. p < p min ; In this case, p is also less than p min. Thus, NP P R p min since 2 p > p max ; In this case, we have p max. There are two cases to consider: a If p max p, NP P R popt p max. b If p < p max, NP P R p < p max. 3 p min p p max ; In this case, we have p. a If p p min, NP P R p min p b If p min < p, NP P R p < p For all cases, we have NP P R popt. REFERENCES.. [] Cisco Systems, Cisco visual networking index: Global mobile data traffic forecast update, 23-28, White Paper, Feb. 24. [2] M. H. Cheung, R. Southwell, and J. Huang, Congestion-aware network and Data offloading, in Proc. of 48th Annual Conference in Information Science and Systems (CISS 24, y f(p p y g(p h(p y g(p Offload probability (p p Fig. 5. Illustration of proof of Proposition 2. [3] J. G. Andrews et al., What will 5G be? IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp , Jun. 24. [4] G. Iosifidis, L. Gao, J. Huang, and L. Tassiulas, An iterative double auction mechanism for mobile data offloading, in Proc. IEEE WiOpt, May 23, pp [5] K. Lee, J. Lee, Y. Yi, I. Rhee, and S. Chong, Mobile Data Offloading: How Much Can WiFi Deliver?, IEEE/ACM Trans. on Networking (TON, vol. 2, no. 2, pp , April 23. [6] L. Gao, G. Iosifidis, J. Huang, L. Tassiulas, and D. Li, Bargainingbased mobile data offloading, IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp. 4-25, Jun. 24. [7] C. W. Patterson, A. B. MacKenzie, S. Glisic, B. Lorenzo, J. Röning, and L. A. DaSilva, An economic model of subscriber offloading between mobile network operators and WLAN operators, in Proc. IEEE WiOpt, May 24, pp [8] A. Li, X. Liao, Z. Gao, and Y. Yang, Price discount strategy for WSP to promote hybrid access in femtocell networks, in Vehicular Technology Conference (VTC Fall, 24 IEEE 8th, Sep., 24, pp. -6. [9] F. Mehmeti and T. Spyropoulos, Performance analysis of On-the-spot mobile data offloading, in Proc. of Globecom 23, 23. [] Y. Kim, K. Lee and N. B. Shroff, An analytical framework to characterize the efficiency and delay in a mobile data offloading system, in Proc. of Mobihoc 4, 24. [] N. Cheng, N. Lu, N. Zhang, X.(S. Shen, J. W. Mark, Opportunistic WiFi offloading in vehicular environment: A Queueing analysis, in Proc. of Globecom 24, 24. [2] O. Simeone, Y. Bar-Ness, and U. Spagnolini, Stable throughput of cognitive radios with and without relaying capability, IEEE Trans. Commun., vol. 55, no. 2, pp , Dec. 27. [3] I. Krikidis, N. Devroye, and J. S. Thompson, Stability analysis for cognitive radio with multi-access primary transmission, IEEE Trans. Wireless Commun., vol. 9, no., pp , Jan. 2. [4] S. Kompella, G. D. Nguyen, C. Kam, J. E. Wieselthier, and A. Ephremides, Cooperation in cognitive underlay networks: Stable throughput tradeoffs, IEEE/ACM Trans. Networking, vol. 22, no. 6, pp , Dec. 24. [5] R. M. Loynes, The stability of a queue with non-independent interarrival and service times, in Proc. Camb. Philos. Soc., vol. 58, pp , July 962. [6] R. B. Cooper, Introduction to queueing theory 2nd ed., Elsevier North Holland, New York, 98. [7] I. Adan, and J. Resing, Queueing theory, Eindhoven University of Technology. Department of Mathematics and Computing Science, 2. [8] S. Boyd and L. Vandenberghe, Convex optimization. Cambridge, UK: Cambridge University Press, 24.