Availability of WDM Multi Ring Networks

Transcription

1 Paper Availability of WDM Multi Ring Network Ivan Rado and Katarina Rado H d.o.o. Motar, Motar, Bonia and Herzegovina Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Univerity of plit, plit, Croatia Abtract hi paper preent a new approach to modeling the availability of the network compoed of multiple interconnected ring in two node. For availability modeling method algebraic formulation i ued. Uing thi method, through the availability of multiple ring network coniting of two and three-ring connected to two node, a general expreion for the availability between two terminal of multiple ring network i derived. o perform the expreion ome real aumption were taken and the analytical calculation howed that the ue of thee expreion under thee aumption provide real value for availability between the two terminal of multiple ring network. Information on the availability of link and node i taken from previouly publihed work. Keyword algebraic, availability, multiple, WDM.. Introduction elecommunication ervice have an important role in the development of modern ociety. Rapid growth in demand for data tranmiion and Internet traffic require highcapacity tranmiion ytem. he only tranmiion media that can meet the need of uch a large capacity i an optical fiber. Unlike other media only the optical fiber ha a large unued capacity that can effectively utilize the technologie baed on wavelength diviion multiplexing (WDM). In uch network, diconnection for any reaon, i.e. equipment failure or human error, can caue iolation in term of telecommunication and profit loe for uer and network operator. herefore, the availability of telecommunication network i becoming a very important factor for network operator. he baic problem i how to enure the urvival of link between two node within large network in term of failure and how to enure high availability. he development of model of reliability and availability of ingle elfrenewable WDM ring have been dealt with by the author in [] uing optical add/drop multiplexer in the node. here are a lot of paper dealing with the calculation of the availability uing the hared-path protection in which it wa concluded that the ue of thee method guaranteed the achievement of availability and pare capacity utilization, which i epecially important for operator a ervice provider []. M. Clouqueur and W. D. Grover [] invetigated how to deign a network that i able to retore the connection of all cae of ingle link failure between any two node in the ring (pan protection) with le invetment. hey alo concluded that ome linked network are very robut to the imultaneou double link failure. ome author invetigated how the availability of ervice depend on the total capacity and on the protection reource allocated amount neceary for matering the protection in the event of failure to the work path [4], [5]. In thi paper, the author will develop model and derive expreion for availability between the two terminal for multiple ring network, tarting from a network coniting of two and three-ring connected to two node example.. Mathematical Bai for Formulation of Network Model.. General Remark on Availability Availability i defined a probability that a ytem i correct at ome point in time, provided that it properly worked at time = 0 and that defective condition appear (maintenance or failure), but are alway repeared and the ytem i operative again. Alo, the availability of a ytem at point in time i defined a the ratio of time for which the ytem i correct in relation to the total time. he Mean ime o Failure (MF) i defined a /λ, where λ i intenity of the failure. It i uually expreed in Failure In ime (FI), and FI mean failure in 0 9 hour. Uing Mean ime o Repair (MR), the availability A can be calculated by [6]: MF A = MF+ MR. () imilarly, the unavailability U i defined a probability complementary to the availability, i.e. U = A, () and it i likely that the ytem i not working properly at ome point in time. When reporting about ytem/network performance, the unavailability i often expreed a Mean Down ime (MD) in minute per year, i.e. MD = U. ().. Method of Algebraic Formulation Although there are everal method uitable for modeling network availability, i.e. elementary path enumeration, in thi paper the algebraic formulation method i ued [6], [7]. 5

2 Ivan Rado and Katarina Rado Intead of working with probabilitie, in thi paper the emphai i on algebraic object (polynomial) and their appropriate tranformation. Let a network G = (N, E) be a directed network with ource node and the detination node t (N node, E edge). uppoe that the node in the network G are ideal and that link m = E are ubject to failure that occur randomly and are repairable. Let each link k =,,...,m be correpond with the variable x k. Furthermore, let x i an event for i m, which indicate that the link e i i in working order then it availability i A i = p[x i ]. Event x, x,..., x m are independent. If x and x are event then x + x are union of mutually excluive event and x x the cae of two independent event. he goal i to calculate the availability of the two terminal and t a repreented by a polynomial function of x element: A t (x) = A t (x, x,..., x m ). (4) which give the exact availability between the two terminal when the appropriate variable x k are replaced by the appropriate link availability A k. o calculate the availability the two new operator i introduced: i ued to repreent the erie combination of two or more element, i ued to repreent the parallel combination of two or more element. he union of arbitrary event x x and product of arbitrary event x x cannot be developed from numerical value, becaue it depend on the individual tatitical correlation or the correlation between two event a oppoed to union of two mutually excluive event, or the product of independent event whoe probability i eaily calculated [8]. Mot of the algebraic approache for availability exact calculation between the two terminal uing the fact that i commutative and the fact that x x = x i and attenuate any repetition of event in product and author replace them by ordinary product. Firtly, the cae where link a and b are connected in erie i conidered. If the link failure are independent, the availability of uch a tructure i equal to the availability of product A a and A b. However, there i a poibility that link contain ome common element. uppoe, for example, that link a contain component x x x 7 and link b component x x x 5. Let A denote the event where component, and 7 are correct and if failure of component are mutually independent, availability i p(a) = A A A 7 and let B denote the event that the component, and 5 are correct and the availability of B i equal to p(b) = A A A 5. Now AB i an event where component,,, 5 and 7 are correct and one link that replace a and b will be marked a x x x x 5 x 7 : x x x 7 x x x 5 = x x (x x )x 5 x 7 = = x x x x 5 x 7. Replacing the variable by adequate availabilitie give the availability of a replacement link A = p(ab) = A A A A 5 A 7. Another operator i applied to link that are connected in parallel, in thi cae, link a and b. If element are working independently with an availability A a and A b their replacement link will have availability A a + A b A a A b. hi formula can be expanded to include poible dependence. For example, let link a include component x x x 7 and link b component x x x 5. Parallel tructure will function properly if either link i correct, and the p(a B) = p(a)+ p(b) p(ab), o that one link that replace a and b will have the variable x x x 7 x x x 5 = = x x x 7 + x x x 5 x x (x x )x 5 x 7. A x i x i = x i then x x = x o it get x x x 7 x x x 5 = = x x x 7 + x x x 5 x x x x 5 x 7. Replacing the variable again by the adequate availability give the availability of alternative link p(a B)=A A A 7 + A A A 5 A A A A 5 A 7. General algebraic um of two polynomial f and g i defined a: f g = f + g (f g). (5) Let repreent the et of all polynomial that can arie by a combination of monomer uing thee two operator, then let (,, ) form a ditribution lattice with the mallet element 0 (zero polynomial) and the greatet element (unit polynomial). For f, g, h to apply the following axiom [9]: f f = f f 0 = f f g = g f f f = f f = f f g = g f f (g h) = ( f g) h f (g h) = ( f g) h f (g h) = ( f g) (f h) f (f g) = f f (f g) = f (6) In order to find a connection between the algebraic tructure and network availability P t i defined a a et of all 54

3 Availability of WDM Multi Ring Network (a) (b) t,, t, t, t t,, t,, (c) (d) t,, t t,, t t,, t,, Fig.. ring. Working path and recovery: (a) without fault, (b) fault within the ring, (c) fault in ide the ring, (d) fault with in two (a) (b) t,, t, t, t t,, t,, (c) (d) t, t, t t,,, t, t,, Fig.. Path of renewal: (a) without fault, (b) fault within the ring, (c) fault in ide the ring, (d) fault with in two ring. elementary -t path P in the network G. It alo define the value of path v(p) a a variable product repreenting the link along the path P v(p) = {x k : k P}. (7) Availability in thi cae i the um of value v(p) over all elementary path from to t A t (x) = P P t v(p). (8) In the operation each link wa included a many time a the number of occurrence in the et P t, of coure, ince thi operator i, before applying the imple product, repetition are eliminated.. Availability of Multi Ring Network Generally, in the multiple ring network the tranmitted ignal between two node and pae N R ring and interconnecting node. he path through, which the ignal pae during normal operation i called a work path. When analyzing renewal path, only thoe path that include ring through, which the working path i paing are taken. Although there are more interconnection ring that could provide connectivity between node and in the cae of failure on the working path, thoe are not analyed becaue path recovery require coniderable amount of time. In thi way only ubnet, which are compried of interconnected ring over the working path are examined, while all other combination are not analyzed. In thi paper, the model of availability were developed and expreion derived for the availability between two terminal of network coniting of two and three ring that are connected to two node. he expreion valid for the network of two and three ring i alo valid for multiple ring network compried of N R a demontrated by mathematical induction... Availability of Network of wo Ring Another focu i the network compried of two ring. A poible failure ite ring, ring and the interconnecting 55

4 Ivan Rado and Katarina Rado (a) n P t,, t,, t,, t,, n (b) n P t,, t,, t,, t, n, (c) n P t,, t,, t,, t, n, (d) n P t,, t,, t,, t, n, Fig.. hree ring network with: (a) no failure, (b) failure of the firt interconnect node, (c) failure of another interconnect node, (d) failure of both interconnect node. node are taken o that there i a total of 7 combination or even renewal path: ( ) ( ) ( ) + + = ++ = 7. Renewal path between node and need not be mutually excluive becaue a parallel um eliminate identical (duplicate) path. For a network compried of two ring there i a work path with no failure and 7 renewal path which are the reult of failure at work path of ring and and primary interconnecting node. uppoe that each ring i compried of N link where there are m working and that the connection between t, t,, and,, i achieved with one link. Figure how working path and recovery path, but with alway correct primary interconnection node. Figure how the path of renewal, but alway with a faulty primary interconnect node. he value of path in failure-free (P 0 ) cae i v t (P 0 ) = (x lr ) m x P (x lr ) m, where x lr and x lr denote link that belong to the firt (index r ) and econd ring (index r ). For each of thee 7 path the renewal are alo defined a the value of path that are marked with v t (P ) (Fig. b) to v t (P 7 ) (Fig. d). Availability i a parallel um of path value when there are no failure and value of all renewal path, which are the conequence of failure, and therefore A t (x) = P i P t v t (P i ). ince the true availability between two node of an individual ring for the tandard ize of ring i approximately equal to the minimum availability [0], o in thi cae availability between the two terminal for the network compoed of two ring i A (x) = (X min X min ) [ x P + x (x P x ) ]. Auming that the ring and interconnecting node alo have no common element, ign could be elided and the common ign of multiplication might be ued ( ) A (x) = X mini [x P + x x P x ]. i=.. Availability of Network of hree Ring A imilar analyi can be implemented for a network coniting of three ring a hown in Fig., taking into account all the renewal path that can occur a a reult of 56

5 Availability of WDM Multi Ring Network failure of each ring part, the interconnection of node and all their poible combination. If the number of poible failure i 5, the number poible combination total i ( ) ( ) ( ) ( ) ( ) = =. 4 5 o avoid examining all poible renewal path, the author take into conideration confirmed fact in ubection. that all failure of individual ring work path renew within themelve, o that the analyi i brought down to the failure of interconnection node, which are only two and therefore the combination number decreae ignificantly: ( ) ( ) + = + =. If it i aumed that all the interconnecting node of the ame type are equal (identical equipment) and auming that the ring and interconnecting node have no common element, imple multiplication ign can be written intead of ign [ ] ]. A (x) = X mini [x P + x x P x i= If the analyi i conducted for a network coniting of 4, 5,..., N R ring, there would be a general expreion for the availability of two terminal of multiple ring network in which the ring are interconnected in two node: [ ] NR ] NR A (x) = X mini (x) [x P + x x P x, (9) i= which mean that the availability between two node of multiple ring network i equal to the product of minimum availability of individual ring and the interconnection of node availability. 4. Numerical Reult Analyi reult are preented on a network conited of two ring to how that the difference i negligible when the actual and minimum availability for individual ring i calculated. Availability data for optical component hown in able are taken from [0]. able how that for the typical ize of ring (6 0 node), difference between the actual availability and the one obtained by taking a minimum availability for each individual ring are in the wort cae of min/year, which i negligible o that the Eq. (8) and (9) can be ued to calculate availability. Note: W i the number of wavelength channel. Even for larger ring with 4 and 6 node, thoe difference were of 0. min/year, which i alo negligible. hi i epecially important for LA contract which et a minimum availability threhold and charge penaltie for exceeding them. able Availability data for optical component Component ymbol Failure rate [FI] Booter amplifier BOA 00 Line amplifier LOA 00 Preamplifier POA 00 Multiplexer MUX 5 W Demultiplexer DEMUX 5 W Optical witch OW 000 Fix tranmitter RX 86 unable tranmitter X 745 Fix receiver RX 70 unable receiver RCX 470 witch W 50 plitter PL 50 Cable (per km) OC Concluion hi paper preent a new approach to modeling the availability of multiple ring network uing an algebraic formulation of working with numeric value. It i hown that the path need not be mutually excluive becaue the ue of operator eliminate duplicate route. he analyi howed that the availability calculation of multiple ring network, in which the ring are connected to two node, i actually reduced to a product of minimum availability of individual ring and the availability of the node interconnection. hi i done with ome realitic aumption and thee are: the ring do not have common element, the interconnection node alo have no element in common and neither ring nor interconnecting node have alo any common element which are the mot common cae in practice, otherwie the protection would not make ene. he analytical reult have confirmed the theoretical analyi o that the derived general expreion for the availability of the two terminal can be ued to analyze and evaluate the multiple ring network availability. Reference [] D. Arci, G. Maier, A. Pattavina, D. Petecchi, and M. ornatore, Availability model for protection technique in WDM network, in Proc. 4th Int. Workh. Deign of Reliable Commun. Netw. DRCN 00, Banff, Alberta, Canada, 00, pp [] L. ong, J. Zhang, and D. Mukherjee, Dynamic proviioning with availability for differentiated ervice in urvivable meh network, IEEE J. elec. Area Commun., vol. 5, no. 4, 007. [] M. Clouqueur and W. D. Grover, Dual failure availability analyi of pan-retorable meh network, IEEE J. elec. Area Commun. (pecial Iue on Recent Advance on Fundamental of Network Management), vol. 0, no. 4, pp. 80 8, 00. [4] M. C. Arie and A. Koter, Cot-efficient tranparent optical network with high connection availabilitie, in Proc. 8th Int. Conf. ranparent Optical Netw. ICON 006, Nottingham, UK, 006, vol., pp [5] W. Yao and B. Ramamurthy, urvivable trafficgrooming with differentiated end-to-end availability guarantee in WDM meh network, in Proc. th IEEE Workh. Local and Metropol. Area Netw. IEEE LANMAN 004, an Francico, CA, UA, 004, pp

6 Ivan Rado and Katarina Rado able Comparion of availability between and when uing the actual availability of the ring and the minimum availability of the ring Number of ring node he actual availability Minimum availability Difference MD [min/year] N=6 N =0 No. link of working path m= m= No. link of working path m= m= No. link of working path m=5 m= N =4 N =6 No. link of working path m= m= [6] L. chwartz, D. rtenky, and G. Cepcianky, Reliability of telecommunication ytem, Univerity of Zilina, lovakia, 00, p. 9 (in lovak). [7] D. R. hier, Network Reliability and Algebraic tructure. New York: Oxford Univerity Pre, 99. [8] J. Jonczy, An algebraic approach to network reliability, Intitute of Computer cience and Applied Mathematic, Univerity of Berne, witzerland, Feb [9] D. D. Harm, A ymbolic algebra environment for reearch in network reliability, Ph.D. thei, imon Fraer Univerity, Burnaby, Canada, ept. 99. [0] I. Rado and L. chwartz, he wort availability a a parameter for deigning and reporting on the network performance, Communication cient. Lett. of the Univ. of Zilina, vol., no., pp. 0 04, 0. Ivan Rado received the B.c. degree in Electrical Engineering from the Univerity of plit, in 98, and M.c. degree from the Univerity of Zagreb, in 000. He received hi Ph.D. from the Univerity of plit, Croatia in 0. In 985 he joined the P (Pot and elecommunication) omilavgrad. ince 99 he work at Department of ranmiion ytem of the H Motar (Croatian elecommunication). Hi reearch interet include: digital tranmiion ytem, optical ytem and network, availability and reliability of telecommunication ytem. He ha publihed 0 paper in international conference proceeding, 4 paper in dometic journal and 7 paper in international journal. ivan.rado@hteronet.ba H d.o.o. Motar Kneza Branimira bb Motar, Bonia and Herzegovina Katarina Rado undergraduated Electrical Engineering and Information echnology on Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Univerity of plit, in 04, and he gained the academic title: Bachelor of cience in Electrical Engineering and Information echnology. At the moment, he i tudying econd level (graduate univerity tudy program) elecommunication and Information echnology on the ame faculty. he ha publihed a paper in dometic cientific proceeding. krado@feb.hr Kroz mrdecac plit, Croatia 58