Receiver Contention Analysis in Asynchronous Transmission High-Speed Multichannel Networks

Transcription

1 Receie Contention Analysis in Asynchonous Tansmission High-pee Multichannel etwoks IOAI E. OUTOURAKI Depatment of Electical & Compute Engineeing ational Technical Uniesity of Athens Zogaphou, Athens REECE Abstact: In this pape we eelop a pefomance moel of the well-known assie sta couple stuctue opeating in a multichannel contol system enionment. The pefomance moel is eelope to eflect the impact of finite numbe of tunable eceies of the en stations in an asynchonous tansmission access metho. The Elang-B fomula fo pefomance loss ealuation is use to analyze the moel an to examine the eceie collision phenomenon. The moel is then use to examine the system pefomance with aying numbe of stations, contol channels an ata channels. Keywos: Waelength Diision Multiplexing(WDM, tunable eceie, electonic pocessing bottleneck euction, eceie collision, Elang- B fomula, aeage ejection pobability.. Intouction The temenous incease in the capacity of hotonic netwoks makes the poblem of the electonic pocessing bottleneck of ital impotance. In esent yeas thee has been a eseach towa the eelopment of waelength iision multiplexing employing a single sepaate contol channel to exchange contol infomation. One of the funamental poblems is the ability of a station to eceie an pocess all contol packets that tansmitte oe the single contol channel. In the stuies of [6-2] a Multichannel Contol Achitectue(MCA using seeal contol channels with suitable meium access techniques ae suggeste to oecome this poblem. On the othe han a class of popose potocols base on anom access esult in low thoughput ue to contentions. Een though most of the popose potocols ty to oecome the contention poblem oe the contol an ata channels fail to achiee high leel of utilization ue to inefficient scheuling scheme that fail to eal with eceie contention. The popose scheme aopts the MCA which euces the effect of electonic pocessing bottleneck an intouce a new etwok Inteface Unit (IU with a finite numbe of tunable eceies at each station. This netwok achitectue with the popose (IU eceases the eceie contentions, impoing the pefomance measues of the netwok. 2. etwok Achitectue an Assumptions The system une consieation as Figue shows is a passie sta netwok. The system uses + waelengths, λ c,..., λc, λ,..., λ, to see an finite numbe M ( M > of stations. The multichannel system at waelengths λ c,..., λc foms the Multichannel Contol Achitectue an opeates as the contol multichannel system while the emaining channels at waelengths λ,..., λ constitute the ata multichannel system. Thus the popose netwok moel with MCA is F escibe as [ CC ] TT [ FR] [ TR]. It means that thee ae contol channels an each station has a tunable tansmitte tune at λ c,..., λc, λ,..., λ. The outcoming taffic fom a station is connecte to one input of the passie sta couple. Aitionally, eey station also uses fixe tune eceies FR one fo each contol channel an F tunable eceies to any of ata channel F λ,..., λ inicate by TR. The incoming taffic to a use station is splitte into + waelengths

2 by a WDMA splitte fom which F of waelengths can be selecte by the tunable eceies as Figue inicates. The tansmission time of a fixe size contol packet is use as time unit (contol slot an the ata packet tansmission nomalize in contol slot time units is L ( L > which is calle ata slot. The popose scheme belongs to the asynchonous tansmission potocols in which the ata channels ae unslotte. The packet tansmission poceue is as follows: A station geneating o etansmitting a ata packet, selects anomly one of the waelengths λ c,..., λc an sens a contol packet oe a λ ci. The contol packet consists of the tansmitte aess, the eceie aess an the waelength t as is shown in Figue. The access metho follows the "tell an wait" policy. By this stategy a ata packet is tansmitte if an only if its coesponing contol packet has successfully tansmitte. If moe than one contol packets use the same contol channel, uing a contol packet ulneable peio, a collision occus (contol channel collision. Figue : assie sta multiwaelength achitectue Also if moe than one ata packets select the same ata channel, to be tansmitte uing a ata packet ulneable peio, a collision occus an all oelapping ata packets (in pat o full ae estoye (ata channel collision. A station will hea the esult of the tansmission of its contol an ata packet by listening to the sta couple multichannel system since it opeates as a boacast meium. In the eceiing moe if a station ientifies its aess as being announce in a contol packet on a contol channel an the coesponing ata packet is tansmitte successfully, immeiately ajusts a eceie to the waelength channel specifie in the contol packet fo ata packet eception. We say that a tunable eceie of a station Z is actie, if it is tune eceiing a ata packet fom a ata channel λ i ( i,...,. It is possible all F tunable eceies of station Z to be actie at a time instant. o any successfully tansmitte ata packet aesse to station Z is ejecte. This phenomenon is calle eceie collision [4-2]. We consie that at any point in time each station is capable of tansmitting at a paticula waelength λ T an simultaneously eceiing at a waelength F TR. Citical components fo the implementation of the popose potocols ae tunable tansmittes an tunable eceies. In pactice the tunable tansmittes an tunable eceies hae tene to hae a fast tuning time o a lage banwith, not both. Tunable waelength filtes ae one of the most impotant builing blocks of WDM netwoks. The filte is the tuning element in tansmittes an eceies. The ieal filte fo WDM netwoks equies fast tuning times (as compae to the packet tansmission times an wie tuning ange an low powe consumption. o the spee an ange of tunable tansmittes set the majo limitations affecting WDM netwoks opeation. In ou analysis we ae not take into account these limitations assuming negligible tuning times an ey lage tunable banwiths. Also in ou analysis we ignoe the effect of popagation elays. tations paticipating in unsuccessful tansmissions, efe thei etansmissions fo a anom time until successful etansmission. We assume unifom istibution of etansmissions. The anom time elay intouce between two consecutie etansmissions is unifomly istibute fom to K time units. Finally the total offee taffic fom new geneate an etansmitte packets obeys to oisson statistics. 3. Analysis Contol channels ae consiee to be slotte with the size of the contol packet. All contol slots ae synchonize in a paallel system constituting the contol multislot. A station esiing to communicate with an othe waits fo the beginning of the next multislot, choose a pai λ, channels an sens ( ci λj

3 fist the contol packet oe the λ ci channel. If the contol channel is tansmitte coectly, the next time unit the station tansmits the ata packet oe the λ j channel. In case of unsuccessful tansmissions on a contol o a ata channel of the system, the stations paticipating in it efe thei etansmissions accoing to etansmission policy. Let the mean offee taffic oe ( channel contol system in a multislot, obeys to oisson statistics. j /, the taffic to j th contol channel j {,2,,} gien that each contol channel is chosen with equal an constant pobability j /. c the pobability of one oisson aial in a contol channel uing a multislot. Then / c e ( A w anom aiable epesenting the numbe of contol packets in a multislot time 0 A w. Thus the pobability of fining A w k contol channels eeyone with one oisson aial uing a multislot, obeys to binomial pobability law. k k [ Aw k] c c k ( (2 c the aeage successful tansmission ate of contol packets in a multislot time in steay state. min( M, / c E{[ Aw ]} k [ Aw k] e (3 k A ata packet is fowae oe a gien ata channel n lets say n, n (,2,..., afte successful tansmission of the coesponing contol packet. We assume that each ata channel is chosen with the constant pobability n /. The ulneable peio fo each ata packet is L time units on each sie of the contol packet. o the total ata packet ulneable peio is 2( L time units. Let 0 the pobability that no one ata packet is tansmitte on a gien ata channel n at i th minislot of the ulneable peio. {- [ obability of successful tansmission of a contol packet fom j th contol channel j {,2... } at the i th multislot whose the accompanying ata packet is estine to the afoementione ata channel n ]} 0 ( c (4 0,ul the pobability that no one ata packet has been estine to station n uing the ulneable peio in steay state. Then 2( L 0, ul 0 (5 f the pobability that at least one ata packet has been estine to ata channel n uing the ulneable peio in steay state. Then f 0, ul (6 In othe wos f is the pobability that at least one collision will take place at the afoementione time inteal. L /, the offee taffic pe ata slot, to the ata channel n. Thus the aeage successful (etansmission ate of ata packets oe a ata channel n pe ata slot in steay state. + (7 f 2( L 0 (8 o L 2( L e [ e ] (9 y xy Using the appoximation ( x e fo small x in (9, we get L e exp[ 2 e ( L ] (0 T the total system thoughput of the system, is efine as the aeage numbe of successful tansmissions of ata packets uing a ata slot time in steay state. T ( 3.2 Receie collision The successfully tansmitte ata packets fom the ata waelengths aie asynchonously accoing to oisson aial pocess at a station Z which belongs to the set,2,... M. We appoximate the output ate of ata packets to the input taffic ate into the system of tunable eceies of each station, with oisson aial pocess [-3]. The mean aial ate is T / M an always a tunable eceie is tune to eceie a ata packet until all F tuneable

4 eceies ae actiate. At this point the incoming successful tansmissions ae ejecte in a F -see loss system. Thus the possibility of actie eceies gies ise to ejection pobability at estination. In this case the block pobability of a ata packet is B an this taffic moel is known as Elang- B fomula. The fixe ata packets length gies constant seice ate / L. B F ( n T / M ( F T / M F! n n! (2 The mean pobability suc, of the successful eception at estination of a ata packet by a station in steay state is gien by suc T ( B (3 M The pobability of fining W j, iffeent stations as estination of coectly eceie ata packets obeys to the binomial pobability law gien by M j j M j [ W j] suc ( suc (4 c the aeage ate of the coectly eceie packets at the estination, uing a ata packet tansmission time L, conitioning on the eceie collision effect. c Le E{[ W ( ]} B M j exp[ 2 j [ W e j] M ( L ] 3. Aeage Rejection obability suc (5 We efine ej, as the aeage ejection pobability at estination, in steay state, the atio of the aeage numbe of ata packets ejecte at estination ue to actie eceies, to the aeage numbe of successfully tansmitte packets oe the multichannel system uing a ata packet tansmission time, then T c ej (6 T 4. Delay D the inteal between the geneation time of a ata packet an the time of successful eception at estination. Data packet elay D, is compose fom thee pats as follows: D Dw + D + L + (7 D w the waiting time fom the geneation of a packet o fom the time instant that a backlogge station ecies to tansmit until the begin of the next multislot. D the elay fom the tansmission of a ata packet until the begin of successful eception at the estination. F the pobability of successful tansmission of a ata packet. Fom (5 we take / / F e ( B exp[ 2 e ( L ] (8 Q (n the pobability of successful etansmission of a packet afte n tials. Assuming that the pobability of success is the same on any ty, n has a geometic istibution, i.e. Q n ( n F ( F (9 R the aeage numbe of tials fo successful tansmission of a contol packet. o R E[ n] e / n exp[2( L nq ( n / F ( B e / ] (20 D b ( K + / 2, the aeage elay between successie etansmissions of contol packets. The aeage packet elay D, is

5 E[ D] E[ D w + ( R ( Db 2 ] + E[ D ] + L L + L + (2 4. umeical Results The optimum pefomance measues with espect to netwok paametes is as follows. We set the fist eiatie of Eq. ( with espect to fo ealuation of the maximum the coesponing. o opt, max an L,max (22 e 2( L opt (23 The opt that maximize the thoughput pe ata channel coespons to an optimum atio of the numbe of the contol an ata packets. Figue 3: The aeage Delay s. the thoughput of the coectly eceie packets fo M50 stations 30 ata channels, 20 contol channels with L0 time units an F,2 tunable eceies pe station. e opt 2( L (24 Figue 2: The aeage ejection pobabilities s. the offee taffic fo M50 stations 30 ata channels, 20 contol channels with L0 time units an F,2 tunable eceies pe station. Figue 4: The aeage Delay s. the thoughput of the coectly eceie packets fo M50 stations fo,2,3 contol channels an 20 ata channels with L0 time units an F tunable eceie pe station an K200 time units. Coesponence of the numeical esults can be obsee in the figues 2-4. Figues illustate the impact of MCA in the pefomance measues as the numbe of contol channels incease. On the othe han it is obious the impoement of the netwok behaio as the numbe of tunable eceie

6 inceases. Ou stuy expans the analysis in a quantitatie basis fo compaison with iffeent netwok achitectues with aious numbe of contol channels an tunable eceies. 5. Conclusions The objectie of this pape is to eelop a efficient netwok moel fo electonic bottleneck euction in conjunction with thoughput an elay impoements. We examine the eceie collision phenomenon on a waelength iision multiplechannel multiple-access potocol tagete to a sta couple photonic netwok. The netwok achitectue has stations with one tunable tansmitte, fixe tune eceies to sense the contol channels an F tunable eceies. The system of finite numbe of tunable eceies(sees at each station is moele as an F-see loss system. Thoughput an packet elay of the popose achitectue ae stuie with aiations in the numbe of tunable eceies, contol an ata channels. Refeences: [] H. Tagaki an L. Kleinock, Output pocess in contention packet boacasting systems, IEEE Tans. Communic., ol.com-33, n., pp9-99, o 985 [2]. Mehaai," efomance an otocol Impoements fo Vey High -pee Optical Fibe Local Aea etwoks Using a assie ta Topology ", J. Lightwae Technology, ol.8, pp , Ap.990. [3] M.I. Habbab, M.Kaeha, an C.E.W. unbeg," otocols fo Vey High -pee Optical Fibe Local Aea etwoks Using a assie ta Topology ",J. Lightwae Technology, ol. LT-5,pp , Dec [4] Ioannis.E.ountouakis, "Thoughput ealuation of multichannel slotte Aloha-type potocols with eceie collisions" Telecommunication ystems ol.5, o.4 pp July 996. [5] I. E. ountouakis, " efomance Ealuation with Receie Collisions Analysis in Vey High- pee Optical Fibe Local Aea etwoks using assie ta Topology ", J. Lightwae Technology, ol.6, o.2 pp , Decembe 998. [6] I. E.ountouakis, " A Multiwaelength Contol Achitectue fo Electonic ocessing Bottleneck Reuction in WDMA, Lightwae etwoks", Compute Communications ol.2 umbe 5-6, pp , eptembe 999. [7] I. E. ountouakis " Waelength Contol otocols fo WDM LA's with Resticte Data Channel Collisions", Intenational Jounal of Communication ystems, ol.3, Issue 4, pp , June [8] Ioannis.E.ountouakis: Design an otocol Analysis fo assie ta Topology of WDM etwok, Micowae an Optical Technology Lettes John Wiley & ons, Lt, ol.25 umbe 3, May 2000 pp [9] Ioannis.E.ountouakis, " Multiwaelength Contol potocols fo WDM etwoks with Resticte Data Channel Collision", Intenational Jounal of Communication ystems, ol.3 Issue 4, pp June [0] Ioannis.E.ountouakis, " Design an Analysis of a ynchonous Tansmission WDMA otocol", hotonic etwok Communication ol.2 umbe 3 pp , August 2000,. [] Ioannis.E.ountouakis, " Asynchonous tansmission potocols fo WDM LAs using multichannel contol achitectue", Compute Communications, ol. 24 umbe 7-8, Apil 200, pp [2] Ioannis.E.ountouakis, " An Efficient etwok Achitectue an otocols fo WDM etwoks ", Euopean Tansactions on Telcommunications, ol. 2 o. 6, oembe/decembe 200, pp