Analysis of Queue Performance of ngbn-arq Improved Protocol Based on TDD Channel

Transcription

1 Iteratioal Joural o Iormatio ad Electroics Egieerig, Vol. 5, No. 3, May 015 Aalysis o Queue Perormace o GBN-ARQ ad Its Imroved Protocol Based o TDD Chael Suoig Li, Ju Yu, ad Yogui Tie, Memer, IACSIT Astract Cosiderig Time Divisio Dulex (TDD) chael with suscetile eviromet ad high acet error rate, this aer maily aalyzes delay erormace o the data trasmissio system taig the -coy GBN-ARQ rotocol. First, comiig the trasmissio characteristics o SR-ARQ ased o GBN-ARQ, we ut orward a imroved -coy GBN-ARQ rotocol which reduces the acet costs eectively. Next, we derive the mea delay idexes o the two systems y solvig the M/G/1 queuig model with vacatios accordig to the method o equivalet delay. We also discuss the eect o the delay erormace aected y widow legth, acet error rate ad coy umer o the two systems i detail. The theoretical aalysis ad simulatio idicate: the imroved GBN-ARQ rotocol ca still wor ormally whe it is alied to the TDD wireless data trasmissio with high chael error rate ad the imroved GBN-ARQ ca cut dow the acet cost ad delay eectively, ad imrove the data trasmissio eiciecy without chagig the origial arithmetic ad icreasig system comlexity. Idex Terms Queuig model, GBN-ARQ, TDD, delay erormace, equivalet service delay, mea acet delay. I. INTRODUCTION With the wide develomet ad alicatio o wireless etwor techology, more ad more commuicatio equimet, such as all ids o remote cotrols, luetooth headset, laystatio ad wireless riter etc., mae use o wireless trasmissio to realize itelliget cotrol. These devices mae our lie ecome coveiet. But ecause o the cost ad the characteristics o them, comlex mechaisms or comoets are ot used i these devices. The data are trasmitted alog the two directios i these small commuicatio systems, ut the trasmissio o a chael is oly oe-way at the same momet. Usually this way o trasmissio is called Time Divisio Dulex commuicatio (TDD) [1]. I additio, some secial chaels such as uderwater acoustic chaels ca oly use the TDD commuicatio ecause o the chael's comlexity, oise itererece ad delay erormace. At reset, research o various data trasmissio cotrol rotocols is mostly limited to the ull dulex commuicatio system, ad it seldom ivolves the TDD commuicatio. Besides, the characteristics o the wireless chael such as time-variatio ad ustale trasmissio ote lead to the declie i erormace o all ids o ARQ retrasmissio mechaism Mauscrit received July 1, 01; revised Setemer 0, 01. This wor was suorted i art y the Natural Sciece Foudatio o Chia uder Grat The authors are with the School o Sciece, Lazhou Uiversity o Techology, Lazhou , Chia ( lsuo@13.com). i the ull dulex li. So it is sigiicat to id a ew id o data trasmissio cotrol rotocol which is more suitale or wireless TDD commuicatio. Now error cotrol rotocols o Automatic Reeat request (ARQ) are used requetly. The delay erormaces o wireless data trasmissio etwee GBN-ARQ ad SR-ARQ systems with ull-dulex are comared i []. I [3], the authors also researched a GBN-ARQ system ad otaied the geeral exressio o mea acet waitig delay ad mea acet service delay. The erormace o the hal-dulex SW-ARQ rotocol ased o water acoustic commuicatio etwor was studied i []. But the aove studies are ased o the coditio o ull-dulex without cosiderig high oise chael. Authors o [5] ad [] did the research o the delay erormace i hal-dulex withi irared-ray commuicatio systems, ad got the geeral exressio o mea acet waitig delay ad mea acet service delay. Actually, they did the research o the cotiuous ARQ (CGBN-ARQ) which is oe o the GBN-ARQ rotocols, ad did't cosider the iluece o eedac delay. As a imrovemet o stadard GBN-ARQ, -coy GBN-ARQ (GBN-ARQ) rotocol is arely used or studied ecause o the icreased acet umer ad cost. But GBN-ARQ has its ow advatage such as the higher eiciecy i trasmissio. I [7] ad [], it was roved that GBN-ARQ had the higher throughut i high error rate o acet, ut the aalysis was ot ased o TDD chael. Cosiderig that the wireless eviromet o TDD is easy to e distured ad its data trasmissio is easy to e suseded which leads to a high acet loss rate, ad the GBN-ARQ has etter trasmissio accuracy o high error rate chael, i this aer we maily ivestigate the erormace o GBN-ARQ system uder TDD with high chael oise. We irst roose a ew GBN-ARQ system y maig aroriate imrovemet o the origial rotocol ased o comiig with the characteristic o SR-ARQ, which does ot icrease the comlexity ad techical requiremets o the system ut decreases the acet overhead eectively. Our aalysis shows that this imrovemet ca reduce the roaility o acet retrasmissio y the seed o geometric growth. The we model the imroved GBN-ARQ system as a M/G/1 queue with vacatio ad resectively aalyze the delay erormaces o the origial ad imroved GBN-ARQ system i terms o the thought o equivalet service delay. At last, y simulatio aalysis i MATLABL, we discuss how the delay erormace is aected y the widow legth, acet error rate ad coy umer o the two systems. Based o the aalysis ad the coclusio o this aer, it is easy to see that the imroved GBN-ARQ system has ovious sueriority i the wireless data trasmissio uder TDD. DOI: /IJIEE.015.V5.5 15

2 Iteratioal Joural o Iormatio ad Electroics Egieerig, Vol. 5, No. 3, May 015 II. N -C OPY GBN-ARQ PROTOCOL AND ITS IMPROVEMENT BASED ON TDD A. Features o TDD Commuicatio with N-Coy GBN-ARQ Protocol TDD trasmissio meas that sedig ad accetig share the same carrier chael, ad trasmissio mechaism is oly oe lae or two-way traic that oe ode seds while the other ode receives at the same momet. Tae irared commuicatio devices or examle, its trasceiver is o the same carrier, so the light rom seder ad receiver is ot isolated, ad sedig sigals ca iterere with the received iut sigals. Whe the emitter seds a light sigal, ad the receiver is i the state o receivig, it will lead to the result that sigals rom other devices are destroyed y the light. Thereore, the irared data li is a TDD mode, which does ot allow or sedig ad receivig data simultaeously [7]. Geerally, most small wireless trasmissio devices trasmit a little data, ad oly eed the receiver to give a resose or the message rom seder. So, the devices should e as simle as ossile as log as they ca wor ormally, ad mostly tae the TDD mode. Most o the curret research is o comlex equimet which has large iormatio caacity y usig the ull dulex chael. So, the study o the trasmissio rotocol with TDD i small device is very ractical ad sigiicat. GBN-ARQ is oe o the most widely used ARQ rotocols. It has ee alied to HDLC, SDLC, ADCCP ad LAPB i DLC rotocol. There are three tyes o GBN-ARQ: stadard GBN-ARQ, -coy GBN-ARQ, ad cotiuous GBN-ARQ. The asic ricile o GBN-ARQ is as ollows: i the seder does t receive the acowledgemets rom the receiver, it ca sed N acets successively. Whe a NAK (egative acowledgmet) is received y seder, the trasmittig o ay ew acet will e stoed, ad the egatively acowledged acet ad its susequet N-1 acets will e retrasmitted. N is a imortat arameter which is called (slidig) widow width. Here, the receiver oly accets the correct order acets. RN is the received sequece umer emedded i the acowledgemet, ad meas the acets eore it are all received successully. The receiver oly eeds to sed a ACK (ositive acowledgmet) or the iggest correct RN istead o sedig a ACK oce a correct acet is received. O the dulex chael the stadard GBN-ARQ ad cotiuous GBN-ARQ have ee itroduced ad researched i detail y the existig literature. This aer maily studies GBN-ARQ ad revised GBN-ARQ ased o TDD i high oise eviromet. Now, we itroduce the ricile o traditioal GBN-ARQ rotocol ased o the TDD chael y taig Fig. 1 with N=, =. Dieret rom the GBN-ARQ ased o ull dulex chael, the GBN-ARQ ased o hal dulex chael is that its seder ad receiver wor i tur y time divisio. At irst, the seder seds out a set o acets accordig to acet widow legth N, ad the retrasmits them without waitig or the resose to the irst trasmissio. The resose just ca reach the seder ater a roud tri time. By this momet, the seder has set out acets. The seder will cotiue sedig a ew set o acets whe receivig a ACK resose. Oce it receives the NAK resose, the seder will go ac stes ad retrasmit the wrog acet (acet i Fig. 1) ad its susequet N-1 acets. So, the seder eeds a uer which ca store N acets i order to retrasmit the wrog acet ad its susequet acets at ay time. Here or the acet which was detected aulty, its susequet N-1 acets will e aadoed whether they are right or wrog. So, the receiver just eeds a uer that ca store oly oe acet. Thereore, the remise o acet retrasmissio i oe trasmissio is there is twice error or the same acet. For acet1 i Fig. 1, although acet 1 has error ut its coy is right, it ca e acceted ad sumitted i the receiver, while acet eeds to e retrasmitted ecause it ad its coy oth have error i trasmissio. Fig. 1. GBN-ARQ rotocol ased o TDD ( N=, =). B. Imroved N-Coy GBN-ARQ Protocol Based o TDD Now comiig the SR-ARQ, the wireless equimet such as cellhoe ad MP have ee equied with high-caacity RAM ad uer device, ad the erormace ad seed o CPU is also imroved sigiicatly. Based o the coditios aove, we ca imrove the GBN-ARQ rotocol so as to it with wireless commuicatio o TDD chael well without chagig the techology ad comlexity o equimet. That is to set the ext trasmissio widow slidig rule o the system: let the correct trasmitted acets retai i the uer o receiver ad the ew widow is to e made o the acets which err at the last trasmissio ad the ew acets. So, the imroved GBN-ARQ is: every eedac resose will e set ater N acets are set; the uer is used to reserve all the acets that are correctly acceted i the last widow ad o loger aado them; the ew sedig widow oly seds the acets that have errors i the last trasmissio ad ew acets, as Fig. shows. Fig.. The imroved GBN-ARQ rotocol ased o TDD (N=, =). Errors occurred i acet 1 ad acet 3 i Fig., so i the ext widow trasmissio, acet 1 ad acet 3 are automatically iserted ito the widow or retrasmissio. The acet is acceted correctly ad stored i the uer o receiver, ad has o eed to e retrasmitted. Through the calculatio ad aalysis o the ollowig, we ca see this simle imrovemet ca eectively reduce the system service delay. 159

3 Iteratioal Joural o Iormatio ad Electroics Egieerig, Vol. 5, No. 3, May 015 III. PERFORMANCE ANALYSIS OF IMPROVED N-COPY GBN-ARQ AND N-COPY GBN-ARQ ON TDD TRANSMISSION A. Perormace Aalysis o N-Coy GBN-ARQ Based o TDD Through the aalysis o the GBN-ARQ system o TDD trasmissio chael aove, we ow that the seder has ee i the idle state ater the irst widow iishes sedig acets ad is waitig or the resose. The receiver is also i the idle state ater sedig resose. The idle time ca e see as a vacatio with legth V. So a acet service delay is a iterval rom the egiig o trasmissio i the data li to the time that the acet is successully acceted y the receiver, which icludes ot oly the irst trasmissio delay t ut also the retrasmissio delay t (that icludes roagatio delay, rocessio delay, ad eedac delay i the data li layer). Thereore, a acet service delay ca e cosidered as a equivalet service delay, which ollows a geeral distriutio ad ca e descried as a M/G/1 queuig model with vacatios. First, some aalysis assumtios ad symols are give as ollows: all the acets arrive at the queue ideedetly accordig to the Poisso rocess with rate λ; the acet service delay is geerally distriuted ad ideedet o each other; the eedac chael is error-ree; the legth o every acet is m uits; the wrog trasmissio roaility o oe acet is ; ad uder the steady state, the rocessio delay o a acet is t i the data li, ad the receiver eedac delay is t. I additio, let X e the equivalet service delay o successul trasmissio ater times retrasmissio or oe acet, ad V e the -th vacatio legth. X ad V ( = 1,,...) are variale sequeces o ideedet ad idetical distriutio resectively. Thus, accordig to [] ad [], the exressio o mea waitig delay W i a M/G/1 queuig model with vacatios is as ollows: W E X E V E V [ ]/ (1 ) [ ]/ [ ] where EX [ ] is the system service itesity, ad E[X], E[X ], E[V] ad E[V ] are the various momets o X ad V resectively. I GBN-ARQ system, a retrasmissio acet is equiroaly located i each slidig widow with the roaility 1/N. So, the mea acet service delay at the irst trasmissio, which meas the receiver is usy, ca e calculated as: 1 m( N 1) T0 mn ( N 1) 1 N The mea equivalet service delay o the times retrasmissio or oe acet is m( N 1) T mn ( 1)( t t )( 1) The equivalet service delay o successul trasmissio or oe acet is m( N 1) X T0 T mn ( 1)( t t ) (1) Because a successul trasmissio or oe acet o -coy meas that there is at least oe right trasmissio or the acet, the roaility o wrog trasmissio or the acet is. So the roaility o right trasmissio or oe acet is t r 1 1 t ; the roaility o times retrasmissio or oe acet, which meas oe right trasmissio ad times wrog trasmissios, is give y ( ) (1 ). The, the roaility o t r successul trasmissio or oe acet (which meas oe right trasmissio ad times wrog trasmissio too) is m( N 1) P X mn ( 1)( t t ) ( ) (1 ) 0, 1,, () The 1 st order momet o X ad d order momet o X ca e resectively calculated as m( N 1) E[ X ] mn ( 1)( t t ) ( ) (1 ) 0 m( N 1) (1 ) ( ) (1 ) ( ) mn 0 0 ( t t )(1 ) ( 1)( ) 0 m( N 1) mn t t 1 m( N 1) [ ] ( 1)( ) ( ) (1 ) 0 E X mn t t m( N 1) t t ( ) (1 ) 0 m( N 1) ( t t ) 0 t t mn ( ) (1 ) 0 ( ) (1 ) mn t t m( N 1) t t ( t t ) m( N 1) t t mn 1 mn t t 1 (1 ) I additio, we tae the slots i a sedig widow as the vacatio legth, that is V =mn. The, 1 st order momet o V ad d order momet o V ca e resectively give y 0 E[ V ] mn (1 ) mn (3) () (5) 10

4 Iteratioal Joural o Iormatio ad Electroics Egieerig, Vol. 5, No. 3, May 015 E[ V ] mn (1 ) ( mn) () 0 Puttig (3), (), (5) ad () ito (1), the acet mea waitig delay i traditioal GBN-ARQ system o TDD ca e otaied as where E[ X ] E[ V ] W (1 ) EV [ ] (1 ) mn m( N 1) mn t t 1 1 m( N 1) 1 t t ( t t ) m( N 1) t t mn 3 mn t t Thereore, the acet mea service delay i traditioal GBN-ARQ system ased o TDD is give y T E[ X ] W, that is m( N 1) mn t t T (1 ) mn m( N 1) mn t t 1 1 The throughut o the system ca e give y [9] (7) 1 1 () T B. Perormace Aalysis o the N-Coy Imroved GBN-ARQ Next, we calculate the delay o the -coy GBN-ARQ rotocol imroved i Sectio II.B o TDD chael. From the aalysis i Sectio II, we ow that the traditioal GBN-ARQ ad the imroved system have the similar trasmissio ricile. The mai dierece is that i the wrog acet requires retrasmissio, the imroved system will ot retrasmit all acets ehid this acet ut oly retrasmit the wrog acet o this widow, ad the acet which has ee trasmitted correctly will e stored i the uer. It is ot oly reducig the acet costs, ut also reducig the delay ad imrovig the throughut o the system eectively. Similarly, ased o the equivalet delay, the imroved GBN-ARQ ca e descried as a M/G/1 queuig model with vacatios. The equivalet service delay o successul trasmissio ater times retrasmissio or oe acet is m( N 1) X m ( 1)( t t ) (9) Because the roaility o successul trasmissio or oe acet still is t r ( ) (1 ), this meas oe right trasmissio ad times wrog trasmissios. So we have the roaility distriutio ad the momets o X as ollows m( N 1) P X m ( 1)( t t ) ( ) (1 ) ( 0, 1,, ) m( N 1) E[ X ] [ m 0 ( 1)( t t )]( ) (1 ) (10) m( N 1) (1 ) ( ) m (1 ) ( ) ( t t )(1 ) ( 1)( ) m( N 1) m t t 1 [ ] [ E X 0 m( N 1) m t t ( 1)( )] ( ) (1 ) m( N 1) t t ( ) (1 ) 0 0 m( N 1) ( t t ) [ t 0 t m] ( ) (1 ) ( ) (1 ) m t t m( N 1) [ t t] ( t t ) m( N 1) t t m 1 m t t 1 1 (11) (1) The slots i a sedig widow are still tae as the vacatio legth, i.e. V =mn. The E[V] = mn, E[V ] = (mn). By uttig the various momets ito (1), the acet mea waitig delay i the imroved GBN-ARQ is: 11

5 Iteratioal Joural o Iormatio ad Electroics Egieerig, Vol. 5, No. 3, May 015 where E[ X ] E[ V ] W (1 ) EV [ ] (1 ) mn m( N 1) m ( t ) t 1 1 m( N 1) 1 t t ( t t ) m( N 1) t t m 3 m t t The mea service delay o the imroved GBN ARQ system ased o TDD is T E[ X ] W m( N 1) m t t (1 ) mn m( N 1) m ( t ) t 1 1 (13) The throughut o the imroved GBN-ARQ system is [9] 1 T IV. NUMERICAL ANALYSIS The TDD wireless commuicatio ca ot trasmit data steadily lie the wired chael. It is easily aected y surroudigs ad has high data loss rate, so sometimes, it does ot oer service ormally or eectively. Most researchers have studied the wireless data trasmissio ased o dulex chael or suosig the ideal circumstace ad ideal error rate or trasmissio without cosiderig other actors which iluece the systematic delay oegligily, such as error rate over the chael, acet legth, ad widow legth etc. So some simulatio aalysis usually alls short o the ractical alicatio. Cosiderig TDD chael, we urther mae the umerical aalysis or the GBN-ARQ system ad imroved GBN-ARQ system i MATLAB, which are more suitale or high error rate eviromets. Whe the ilueces o coy umer, widow legth ad acet legth o the system delay were comrehesively tae ito accout, we comared the erormaces o the two systems y umerical aalysis ased o the results o () ad (13) with t =t =1,λ=0.0. Fig. 3-Fig. 5 give the simulatio results which agree with the arameter ractical meaig ad the coditios o the system steady state. mea acet service delay(t) The legth o widows(n) The umer o acet coy() Fig. 3. The legth o widows ad the umer o acet coy versus the mea acet service delay o the GBN-ARQ. mea acet service delay(t) The legth o widows(n) The umer o acet coy() Fig.. The legth o widows ad the umer o acet coy versus the mea acet service delay o the GBN-ARQ. Mea acet service delay T(uit time) GBN-ARQ(=,N=5) GBN-ARQ(=,N=) SGBN-ARQ(=,N=5) SGBN-ARQ(=,N=) The roaility o acet error Fig. 5. Mea acet service delay versus acet error roaility. The comariso etwee the Fig. 3 ad the Fig. shows: whe the system is i the steady state ad the acet trasmissio error rate is ixed, the widow legth ad the coy umer have the same eect tred to the delay o the two systems o coditio that the acet arrival rate, data li trasmissio delay, eedac delay ad vacatio legth are equal resectively. The acet mea service delay is gettig larger as the widow legth ad the coy umer are 1

6 Iteratioal Joural o Iormatio ad Electroics Egieerig, Vol. 5, No. 3, May 015 gettig larger. O the other had, whe the widow legth ad coy umer are gettig smaller, the delay o imroved GBN-ARQ mechaism is ar smaller tha the GBN-ARQ s; whe the widow legth ad coy umer are gettig larger, the delay icreasig rate o the imroved GBN-ARQ is ar smaller tha the GBN-ARQ s. Besides, the sesitivity o the throughut o the imroved GBN-ARQ system to the widow legth ad the coy umer is smaller tha the GBN-ARQ s. Comared to the imroved GBN-ARQ, the GBN-ARQ mechaism has to cut dow its slidig widow legth ad acet umer to attai the same system throughut, ut this will lower the data trasmissio eiciecy. So we ca get the ollowig coclusio: cosiderig the ixed acet legth ad the acet arrival rate, the est error-cotrol solutio to raise the system trasmissio caacity without icreasig the system comlexity is taig the imroved GBN-ARQ rotocol i wireless trasmissio ased o TDD. Accordig to the acet mea service delay i Fig. 5, the GBN-ARQ mechaism ad the imroved GBN-ARQ mechaism have o ovious dierece uder the same simulatio circumstace whe the error rate is lower. As the acet trasmissio error rate icreases, the mea service delay o the two systems also icreases yet ad the icreasig rate o the GBN-ARQ is ar larger tha the imroved GBN-ARQ s. That is to say: the imroved GBN-ARQ mechaism ca still e alied to data trasmissio ormally whe system is i the ad chael eviromet ad the acet error rate is high. Next, the variace o the acet service delay to the GBN-ARQ is larger uder the coditios o the coy umer = ad the widow legth N=5 ad N=, ad the delay variace o the imroved GBN-ARQ is very small. This illustrates that the imroved GBN-ARQ mechaism is more suitale or egieerig alicatio ecause it ca eectively elimiate the cosumtio o system throughut which is caused y icreasig acet costs i the GBN-ARQ system. O the other had, ecause the otimal widow legth ad coy umer ca e determied rom (7) ad (13) cosiderig the ojective o otimal mea service delay, y comrehesively aalyzig o Fig. 3, Fig. ad Fig. 5, we ca get the chagig rule o the otimal slidig widow ad coy umer uder coditio o give trasmissio arameter, that is the otimal slidig widow legth ad coy umer will icrease with the raise o trasmissio accuracy rate o chael ad the system delay. Hece, the imroved GBN-ARQ rotocol ca ot oly e alied i ad wireless chael ut also achieves a id o adative cotrol to system delay y selectig widow legth ad coy umer. V. CONCLUSION Cosiderig small wireless trasmissio devices eig used widely without comlex mechaism, this aer estalishes a M/G/1 queuig model with vacatio or the GBN-ARQ rotocol ad its imroved rotocol ased o TDD trasmissio ad the thought o equivalet service delay. We aalyze the erormace characteristics o the two systems theoretically, derive their mea service delay ad throughut y solvig M/G/1 queuig model with vacatio, ad mae a comuter umerical aalysis o the delay iluece actors such as chael error rate, acet legth, ad widow legth etc. i MATLAB. The theoretical aalysis ad simulatio idicate: the imroved GBN-ARQ rotocol ca still wor ormally whe it is alied to the TDD wireless data trasmissio with high chael error rate. Meawhile, the imroved GBN-ARQ ca cut dow the acet cost ad delay eectively, ad imrove the data trasmissio eiciecy without chagig the origial arithmetic ad icreasig system comlexity. Moreover, y the aalysis results o this aer, the wireless commuicatio system ca achieve automatically adjustig its trasmissio atter y meas o detectig chael circumstace, widow legth ad acet coy umer i egieerig. So, the research ca rovide with some theoretical asis ad aroach or desigig the otimal wireless commuicatio states. ACKNOWLEDGMENT May thas to Pro. Dr. Marty Warre at America East Texas Batist Uiversity or a careul chec o this aer. REFERENCES [1] X. R. Xie, Comuter Networ, th ed., Beijig: Pulishig House o Electroics Idustry o Chia, 003, (I Chiese) [] S. P. Li, C. M. Liu, ad Z. P. He, Research o the delay erormace o GBN-ARQ ad SR-ARQ systems i wireless data trasmissio, Sigal Processig o Chia, vol. 5, o. 3,. 3-3, 005. (I Chiese) [3] S. P. Li ad C. M. Liu, Aalysis o the delay erormace o -ARQ system with vacatios, Joural o System Egieerig o Chia, vol. 3, o. 3, , 00. (I Chiese) [] M. S. Gao, J. R. Lu, ad W. D. Jiag, A id o uderwater acoustic commuicatio o adative ARQ scheme, Data Acquisitio ad Processig, vol. 0, o., , 005. [5] E. G. Varthis ad D. I. Fotiadis, A comariso o sto-ad-wait ad Go-Bac-N ARQ schemes or IEEE0.11e wireless irared etwors, Comuter Commuicatios, vol. 9, o. 10, , 00. [] A. M. Shah, S. S. Ara, ad M. Matsumoto, A imroved selective Reeat-ARQ scheme or IrDA lis at high it error rate, i Proc. th Iteratioal Coerece o Moile ad Uiquitous Multimedia,. 37-, 005. [7] S. P. Li, K. Ji, K. Wu, ad Y. Wei, Delay aalysis o trucated cooerative SW-ARQ ased o Geom/G/1 queue model with radom vacatio, Joural o Comutatioal Iormatio Systems, vol. 9, o., , 013. [] M. Y. Choi, Y. D. Yao, ad H. Hees, Throughut aalysis o a class o selective reeat ARQ with mulit-coy retrasmissios, i Proc. the 001 IEEE Vehicular Techology Coerece, 001, [9] A. Mehta, D. Kagaris, ad R. Viswaatha, Throughut erormace o a adative ARQ scheme i rayleigh adig chaels, IEEE Trasactios o Wireless Commuicatios, vol. 5, o. 1,. 1-15, 00. Suoig Li is with the School o Sciece at Lazhou Uiversity o Techology, Chia. He received the Ph.D. degree i sigal ad iormatio rocessig rom Beijig Jiaotog Uiversity, Chia, i 00. He also got a M.Sc. degree i stochastic model with alicatios rom Lazhou Uiversity i 199, ad B.Sc. degree i mathematics rom Northwest Normal Uiversity i 19. He was a visitig scholar at the Swiss Federal Istitute o Techology Zurich rom May 007 to May 00. He also is a visitig roessor at East Texas Batist Uiversity rom Aug. to Dec His rimary research iterests iclude stochastic cotrol theory ad stochastic rocess; error cotrol theory ad data commuicatio rotocol; hyrid dyamic systems modelig, cotrol ad simulatio. 13

7 Iteratioal Joural o Iormatio ad Electroics Egieerig, Vol. 5, No. 3, May 015 Ju Yu is with the School o Sciece at Lazhou Uiversity o Techology. His major is oeratioal research ad cyeretics. He received the BS degree i alied mathematics rom Zhouou Normal Uiversity i 009. His research iterests are i the areas o stochastic modelig aalysis o wireless commuicatio systems ad hyrid dyamic systems modelig, cotrol ad simulatio. Yogui Tie is with the School o Sciece at Lazhou Uiversity o Techology. His major is oeratioal research ad cyeretics. He received the BS degree i alied mathematics rom Beiag Uiversity o Natioality. His research iterests are i the areas o stochastic modelig aalysis o wireless commuicatio systems ad hyrid dyamic systems modelig, cotrol ad simulatio. 1