Calculation and Simulation of Message Delay on TDMA Short-wave. Communication Network

Size: px

Start display at page:

Download "Calculation and Simulation of Message Delay on TDMA Short-wave. Communication Network"

Emory Bell
6 years ago
Views:

1 Aug. 6, Volume 3, No.8 (Serial No.) Joural of Commuicatio ad Computer, ISSN , USA Calculatio ad Simulatio of eage Delay o TDA Short-wave Commuicatio Network Hairog Ya, Guoji Su, Ya Zhag 3 (, State Key Laboratory for aufacturig Sytem Egieerig, Xi a Jiaotog Uiverity, Xi a 749, Chia;,3 Departmet of Computer, Xi a Ititute of Techology, Xi a 73,Chia) Abtract: TDA protocol i a mai chael acce method of wirele etwork ued i military field, which work by dividig a radio frequecy ito time lot ad allocatig lot to multiple call. Two mathematical model are propoed to calculate the meage delay. Baed o aalyi, the meage delay i the queue of TDA i compoed of two part, oe ca be calculated o // theory, i which the waitig time i from the meage comig ito beig to it beig the header of the queue, the other ca be modeled by the uiform ditributio ad Erlag ditributio, i which the meage waitig time i caued by the header waitig for it tur to be et. Simulatio reult are compared with two method, ad Erlag ditributio i cloer to the imulatio reult tha uiform ditributio. * Key word: RF Network; TDA; Simulatio; eage Delay. Itroductio Radio frequecy tramiio betwee.5 Hz ad 3 Hz i called high frequecy (HF) or hortwave radio commuicatio. HF i widely ued for log ditace tramiio ice the ivetio of radio by arkoi ad Popov, ad growig depite the fat developmet of cellular ad atellite commuicatio ytem. It the oly way of achievig global commuicatio coverage without uig expeive terretrial ad atellite ifratructure. From the ed of 98, the reearch o hort-wave Hairog Ya (97- ), female, aociate profeor, PhD cadidate, viitig cholar i Japa, memberhip of Chiee Aociatio for Sytem Simulatio; mai reearch field: etwork imulatio, ditributed ytem ad mobile etwork. Guoji Su (936- ), male, PhD, profeor; mai reearch field: modelig ad imulatio of complex ytem, virtual reality ad virtual maufacturig. 3 Ya Zhag (974- ), female, lecturer, ater; mai reearch field: etwork imulatio. commuicatio etwork ha attracted wide attetio. I 98, ad hoc etwork baed o HF were propoed i America, called HF-ITF, which i highly detroy-reitat ad flexible. Short-wave commuicatio etwork developed fat i North Atlatic Treaty Orgaizatio (NATO) ad America i 99. Cooperatio ad itercommuicatio of differet etwork are coidered, ad exitig protocol of the wired etwork are ued i the wirele etwork, e.g. TCP/IP, TDA. 998, military govermet of America modified IL-STD-87-7C ad IL-STD-88-4C. The purpoe of the modificatio i to improve the autoimmuizatio of HF to upport the big area battlefield etwork ad improve the cooperatio of the C 4 I. Now, HF techology i till the mai method of the mobile commuicatio i Army, ad TDA i alo the mai chael acce way of the radio tatio commuicatio. Simulatio i the major reearch method of moder war. Through imulatio, the performace of a certai cee ca be aalyzed, ad it ca be foud out if the et cofiguratio are fit. For C 4 I ytem, meage delay i the mot importat parameter. The delay that a packet i TDA protocol uffer ha three compoet [] : ) Acce delay: Thi i the time betwee it arrival ad the ed of the frame time, jut becaue the queue ize i oly meaured at the ed of each frame. 58

2 Calculatio ad Simulatio of eage Delay o TDA Short-wave Commuicatio Network ) Propagatio delay (τ ): The time it take for a bit to reach it detiatio excludig acce time ad queuig delay. Thi kid of delay ca be kow i advace. 3) Queuig delay: Thi i the amout of time for which the packet mut wait i the queue o that the packet that arrive before it are tramitted. Whe packet arrive uiformly durig each frame time, the average acce delay will be half of the frame time, T /, where i the umber of lot per frame. Throughout thi paper, the acce delay i coidered a T /. The total delay i D = T / + T + W where, W q i the queuig delay. Therefore, how to evaluate the queuig delay for the model i what thi paper care about. Rubi [,3] dicued the delay by arkov proce, it i complex, ad for ome aumptio. Thi paper propoe a eaier way to calculate the queuig delay. Thi paper i orgaized a follow. Sectio itroduce workig mechaim of TDA ad calculate the meage delay by aalyi. Sectio 3 give the TDA imulatio reult ad compare the reult with that gotte from the formula of ectio at differet cee. It how that they are very cloe. Sectio 4 give three propagatio model ued i the imulatio. Sectio 5 coclude thi paper.. eage Delay i the Queue of TDA TDA i a techology for deliverig digital wirele ervice uig Time-Diviio ultiplexig (TD) []. TDA work by dividig a radio frequecy ito time lot ad the allocatig lot to multiple call. I thi way, a igle frequecy ca upport multiple, imultaeou data chael. A Frame i T ecod Slot Slot Slot Fig. TDA Frame Structure q.. 3 Fig. TDA eage Queue Coider a TDA ytem i which time i lotted ad time lot are orgaized ito frame, lot are idexed from to, a how i Fig.. The packet have bee divided accordig to time lot. Each data packet ca be et i oe lot. The if it take T ecod to ed oe packet, it will take T ecod to ed oe frame (the queue i ot empty). Each tatio ha a buffer to tore the arrivig meage. Iformatio i aumed to be tramitted through the chael at a bit rat of C bit/. The arrivig traffic form a Poio proce. Poio radom variable are with parameter λt, where T i the duratio of the lot. I other word, the arrival time of the packet form a Poio proce with rate λ. eage arrivig are recorded at the ed of the frame tramiio [4]. The ervice time ditributio of a meage i egative expoet, where u i the mea. Let B repreet the packet ize i bit, ad let C repreet the chael peed i bit per ecod, the the packet tramiio time i T =B/C. Aume that the duratio of each lot i exactly the ame a the tramiio time of oe packet. Coider the queue i oe tatio of TDA. If oe packet wat to be et, it will wait to be the header of the queue, ad it caot be et util the tatio time lot arrive. So, the delay i the queue of TDA i differet with the queue theory of //. It i cocluded the calculatio of the delay i a follow: W q = W q + W q where, W q i the meage delay i the queue; W q i the delay that ca be calculated by the queue theory, which i the period while the meage move to the header of the queue; W q i the delay while the meage i at the header of the queue, ad wait for the tur of hi tatio time lot. 59

3 Calculatio ad Simulatio of eage Delay o TDA Short-wave Commuicatio Network Firt, W q i calculated. Suppoe that the packet arrive at Poio ditributed of λ. Accordig to the character of TDA, the header of the queue i evered after a certai period. The legth of the period i the legth of frame (T ). If the meage queue of oe tatio i take a a // queue, that mea the ervig time of the // queue i T, a certai legth of the ervig time, the rate of the arrival i λ, the ervig rate i μ, μ=/(t ), accordig to little formula, the calculatio i gotte a follow: W q = λ /[ μ( μ λ)] = λ( T ) /[/( T ) λ] = λ( T ) /[ λ( T )] If the arrival of each tatio i uiform ditributio, the waitig time of the ytem icludig tatio i till W q. The ame a the ytem queue legth, it i the value of oe tatio queue legth for uiform ditributio. L ql i the average queue legth. L q λ ( λt ) = = μ ( μ λ ) λt The ecod part of delay of the meage, which i at the header of the queue waitig for it tur, ca be calculated a follow. Theorem The waitig time that the evet at the header of the queue wait for it lot to be et i TDA follow Erlag ditributio. Proof Fig. 3 how time equece of the evet E. A uppoed before that cutomer arrive at a ervice tatio accordig to the Poio model, o the evet arrival time iterval W i (,,) follow expoetial ditributio [5]. Whe -th evet (E ) happe there are - evet happeig. From the begiig of the imulatio, the firt evet (E ) will happe after W, the the time at which E happe i +W =W, the the ecod evet (E ) will happe after E ad waitig for W time iterval, that i to ay, the happeig time of E i W + W, ad o o, the -th evet (E ) will happe at time W +W + +W - +W. A it i kow, W i follow expoetial ditributio, ad Erlag ditributio repreet the um of a erie of expoetial ditributio, o W +W + +W - +W follow Erlag ditributio. W W W 3 W (-)/μ E be the header of the queue D E E E 3 E - E T T T T T d d Whe E happe, it will wait util other previou - evet are proceed to be the header of the queue. A propoed before, the proce rate i μ, the the time for which it wait to be the header of the queue equal to (-)/μ. Here do ot coider two or more evet happeig at the ame time. At the TDA mechaim, μ=/t, T i the time oe frame tramittig, a cot. The meage at the header of the queue will ot be et at oce, for it will wait it Fig. 3 The Time Sequece of E lot. The dah lie of Fig. 3 repreet the real edig time of the evet. So, the -th evet at the header will wait D to be really et. D i calculated by the formula, D = T d = T mod(( Wi T mod(( + ( ) / μ), T ) = W + ( ) T ), T ) = T mod( i where, mod (a,b) i a mod b, ad mod(a,b)<b. W, T) i 6

4 Calculatio ad Simulatio of eage Delay o TDA Short-wave Commuicatio Network A decribed before that follow Erlag ditributio, ad i the formula calculatig D, T i a cot, o D alo follow Erlag ditributio. E(D )=/λ, if [,N] i take a a cotiual umber, N=Tλ, N i the mot meage umber i T. Accordig to the aumptio, here, t i the max waitig legth, T ; N i the poible arrival evet durig time t, equalig to λt. So, E ( D) = E ( N = D ) = N λ N W i d = T / It i the ame a the expected value of uiform ditributio, o the ecod part ca be calculated uig uiform ditributio. So W = λ ( T ) /[ λ( T )] T / q + If the reult are ot ued, the Erlag ditributio fuctio i ued F( t) = j= i ( λ t) e λt /( j!) The formula how that there are evet happeig before t. Accordig to the aumptio, here, t i the max waitig legth, T ; i the poible arrival evet durig time t, equalig to λ T. The tage Erlag equatio are ued to proximate, F( t) = e te λt λt λ the the average waitig time W q, W q = F( t) / ( e = ( e λt λt e λte λt ) / ) /( λt ) Evetually, the total average delay by Erlag ditributio, W q = λ( T ) + ( e /[ λ( T )] λt e ) /( λt ) 3. TDA Simulatio ad Reult Compario I military ad-hoc etwork, the mai topology i how i Fig. 4. Group Gateway Node Fig. 4 Ad-hoc Network Topology Oe of the ubet i abtracted to be the reearch object. I thi model, there are eight hort-wave tatio ad oe cotrol ceter, a how i Fig. 5. Each tatio i imi-dulfux. All meage mut be tramitted through the ceter ode. Node Node 3 Node Node 8 Ceter Node Node 4 Node 5 Node 7 Node 6 Fig. 5 Simulatio Topology Evet chedule i ued ad the TDA mechaim i followed. It take all the procedure of the imulatio a a et of time order evet, ad with the time icreaig, do the evet oe by oe till all the evet are proceed. There are three kid of evet i the imulatio: packet arrival evet, packet edig ad packet receivig. Every evet ha it happeig time. After oe evet occur, the tate of the ytem will chage ad oe more evet trig. All evet are tored i a evet chedule table. VC++ thread i ued to implemet the mechaim. I the imulatio, chael rate i C=4, 96 bit/ [6], correpodig to μ=.5,.8. Take C=4 bit/ for example, the legth of oe imulatio packet i 6 8 bit. The oe lot legth i T =64 8/4=.. The total tatio umber of the ytem i 9, o the frame legth i T =.89. That mea the peed of the proce of the erver i u=/t /=.5. Do the imulatio uder table ituatio [5] whe 6

5 Calculatio ad Simulatio of eage Delay o TDA Short-wave Commuicatio Network λ p u. The compario of the imulatio ad uiform reult i four chael rate i how i Fig. 6 meage daly() μ=.5 uiform model meage delay imulatio meage delay λ(packet/) meage delay () μ=.8 uiform model meage delay imulatio meage delay λ (packet/) Fig. 6 Compario of Simulatio ad Uiform Ditributio Calculatio Reult Reult of mathematic formula ad imulatio are imulatio reult. cloed i differet chael rate. Red lie are the meage delay() μ=.5 Erlag model meage delay imulaito meage delay λ(packet/) μ=.8 4 meage delay() Erlag model meage delay imulatio meage delay λ (packet/) Fig. 7 Compario of Simulatio ad Erlag Ditributio Calculatio Reult I Fig. 7, the Erlag ditributio reult of the two chael rate are compared with imulatio reult. To aalyze, two model ad imulatio reult are compared by u=.5, a how i Fig. 8. From Fig. 8, it ca be ee that, whe u=.5, uder table ituatio, imulatio reult almot tally with the mathematical model. 6

6 Calculatio ad Simulatio of eage Delay o TDA Short-wave Commuicatio Network meage delay () imulatio reult calculatio reult by Erlagia ditributio calculatio reult by uiform ditributio λ (packet/) Fig. 8 The value of uiform ditributio model i a little higher tha that of imulatio reult. The reao i that T / i ued to approximate the delay of the head packet gettig it tur, which i larger tha the reality. The uiform i the ditributio for cotiual model, while Erlag i for iteger model. Let u=.5, λ =.5, for example, N=Tλ=.8, i Erlag model N, =, but i uiform ditributio, evet umber ca take the value from to.8 cotiuouly. The followig i the real data of calculatio. If Erlag ditributio i ued, wq, lambda=.5,wq=.4536 lambda=.,wq= lambda=.5,wq=.9 lambda=.,wq=.4955 lambda=.5,wq=.7548 lambda=.3,wq=.987 lambda=.35,wq=.7459 lambda=.4,wq=.3455 lambda=.45,wq=.489 lambda=.5,wq=.5997 but i uiform ditributio wq=t*m/=.96. It i bigger tha ay of the data from the Erlag ditributio. The value of Erlagia ditributio i lower tha that of uiform ditributio, but cro to the imulatio reult. That i the reao why it ue the two tage equatio. Variace of the uiform ditributio to imulatio i.9, ad that of Erlag i.7. So Erlag i cloer to the imulatio reult. μ=.5 Average eage Delay Compario Ad the imulatio i doe uder the utable ituatio. The imulatio reult jump up a predictio. 4. Cocluio I cocluio, TDA mechaim i aalyzed, ad two type of the meage delay calculatio formula are gotte. It i proved that the waitig time of the header waitig for it time lot follow Erlag ditributio. Queue delay calculatio i propoed ad the reult with imulatio are compared. The reult are cloe. It prove that the method i believable. Ad the little departure eem to be produced by calculatig the delay of waitig to be et. Referece: [] Sirikiat Ariyaviitakul, Fugchag Li, Performace of Uequalized Frequecy-Hopped TDA o Diperive Fadig Chael, Iteratioal Joural of Wirele Iformatio Network, Vol. (), 994: pp [] IZHAK Rubi, eage Delay i FDA ad TDA Commuicatio Chael, IEEE Traactio o Commuicatio, Vol. 7(5), 979: pp [3] Rubi, Z. Zhag, eage Delay Aalyi for TDA Scheme Uig Cotiguou-lot Aigmet, IEEE Traactio o Commuicatio, April, Vol. 4, 99: pp [4] Theodore S. Rappaport, Wirele Commuicatio: Priciple ad Practice (Secod Editio), Publihig Houe of Electroic Idutry. [5] Youzhao Sheg, Queue Theory ad It Applicatio o Computer Commuicatio, Beijig Uiverity of Pot ad Telecommuicatio Publihig Compay, (I Chiee). [6] A. G. Qurehi, Impact of Wirele Acce o Traffic Statitic, Fifth Iteratioal Sympoium o Sigal Proceig ad It Applicatio, ISSPA'99, Bribae, Autralia, -5 Augut, 999: pp (Editor: ark, Fraci, Sabria) 63

20. CONFIDENCE INTERVALS FOR THE MEAN, UNKNOWN VARIANCE

20. CONFIDENCE INTERVALS FOR THE MEAN, UNKNOWN VARIANCE If the populatio tadard deviatio σ i ukow, a it uually will be i practice, we will have to etimate it by the ample tadard deviatio. Sice σ i ukow,