Ehacemet of the IEEE 8.5. MAC Protocol for Scalable Data Collectio i Dese Sesor Networks Kira Yedavalli Departmet of Electrical Egieerig - Systems Uiversity of Souther Califoria Los Ageles, Califoria, 989 Email: kyedaval@usc.edu Bhaskar Krishamachari Departmet of Electrical Egieerig - Systems Uiversity of Souther Califoria Los Ageles, Califoria, 989 Email: bkrisha@usc.edu Abstract We fid that the IEEE 8.5. MAC protocol performs poorly for oe-hop data collectio i dese sesor etworks, showig a steep deterioratio i both throughput ad eergy cosumptio with icreasig umber of trasmitters. We propose a chael feedback-based ehacemet to the protocol that is sigificatly more scalable, showig a relatively flat, slowchagig total system throughput ad eergy cosumptio as the etwork size icreases. A key feature of the ehacemet is that the back-off widows are updated after successful trasmissios istead of collisios. The widow updates are based o a optimality criterio we derive from mathematical modelig of p-persistet CSMA. I. INTRODUCTION IEEE 8.5. is a importat stadard for low-rate lowpower wireless persoal area etworks that is i icreasig commercial use for a diverse rage of embedded wireless sesig ad cotrol applicatios. The stadard provides specificatios for both the physical layer ad the medium access cotrol (MAC) protocol. We characterize the performace of the IEEE 8.5. MAC for oe-hop data collectio i a star topology where there are multiple trasmitters ad a sigle receiver. Our primary focus is o settigs where the umber of trasmitters is large. Because 8.5.-eabled devices are meat to be low-cost ad operate at relatively low rates, such dese deploymets are of iterest i may sesig applicatios ivolvig these devices. We model the IEEE 8.5. as a p-persistet CSMA with chagig trasmissio probability p. We derive the optimal trasmissio probabilities to maximize the throughput ad miimize eergy cosumptio i p-persistet CSMA. We show that, particularly for large umber of trasmitters, the ratio of the expected idle time betwee successful receptios to the expected time betwee successful receptios is a costat for a give packet size whe the trasmissio probabilities are optimal. Further, we fid that whe the trasmissio probability is lower (higher) tha the optimal, the ratio is Kira Yedavalli is curretly with Cisco Systems Ic. i Sa Jose, Califoria. This work was fuded i part by NSF through grats umbered CNS-3555, CNS-376, CNS-678, CNS-35875. higher (lower) tha this costat. This yields a distributed chael feedback-based cotrol mechaism that chages the trasmissio probabilities of odes dyamically towards the optimal. We develop a ehaced versio of the IEEE 8.5. MAC protocol usig this feedback scheme. I our modelig ad evaluatio, we cosider two extremes of the oe-hop data collectio spectrum i dese sesor etworks: oe-shot ad cotiuous data collectio. I oeshot data collectio, each ode seds oly a sigle packet (this could be the respose to a oe-shot query) ad oce that packet is trasmitted the ode is o loger i cotetio for the chael. I cotiuous data collectio, we assume that each ode is backlogged, i.e. always has a packet to trasmit. I both cases, we fid that the IEEE 8.5. protocol performs poorly i dese settigs, showig a steep reductio i throughput ad icrease i eergy with etwork size. I cotrast, the ehaced protocol that we propose is sigificatly more scalable, showig a relatively flat, slow-chagig total system throughput ad eergy as the umber of trasmitters is icreased. This is illustrated i figure. Throughput (Kbps) Eergy (mjoules) 8 6 Packet Legth = 5 Bytes IEEE 8.5. Ehaced IEEE 8.5. 5 55 6 65 7 75 8 85 9 95 Number of Cotedig Nodes 8 6 IEEE 8.5. Ehaced IEEE 8.5. 5 55 6 65 7 75 8 85 9 95 Number of Cotedig Nodes Fig.. Performace of Proposed Ehacemet compared to IEEE 8.5. for Cotiuous Data Collectio The rest of this paper is orgaized as follows. I Sectio II we preset a overview of IEEE 8.5. ad model it as a p-persistet CSMA with chagig p. I Sectio III we preset the modelig ad optimizatio of p-persistet CSMA ad
characterize the performace of the IEEE 8.5. MAC i Sectio IV. I Sectio V we preset a chael feedback-based medium access cotrol techique ad adapt it to preset the ehaced IEEE 8.5. MAC. I the same sectio we discuss directios of our future work. We coclude i Sectio VI. II. IEEE 8.5. I this sectio we preset a overview of the IEEE 8.5. MAC ad model it as a p-persistet CSMA MAC with chagig p. A. Overview & Related Work The IEEE 8.5. stadard ([6]) allows differet etwork topologies such as oe-hop star ad multi-hop. We cosider the oe-hop star topology with multiple data sources ad a sigle sik. I the star topology, a global sychroizatio of odes is assumed ad the time is separated by beacos trasmitted by a etwork coordiator. The beaco-iterval cosists of a superframe ad a optioal eergy savig time i which the odes switch off their radio ad go to sleep. The superframe is divided ito 6 time slots of δ = 3 µsecs duratio each. The superframe cosists of a cotetio access period (CAP) ad a period of guarateed time slots (GTS). The GTS is dedicated for low latecy applicatios. I this paper we cosider oly the CAP mode (without the eergy savig mode, GTS, ad beacos) where medium access is through slotted CSMA/CA. I slotted CSMA/CA, a ode ca trasmit its packet oly after it seses the chael free for a cotetio widow (CW) of time slots. The mai purpose of the CW is to avoid collisios betwee ackowledgemet packets (ACKs) from the sik ad data packets from the sources as the protocol does ot specifically provisio time slots for ACKs [6]. A ode chooses a time slot uiformly at radom from a iitial widow of [, BE ], where BE is the back-off expoet with a iitial value of 3. The ode trasmits its packet if the chael is sesed to be free i that ad the ext time slots; if the chael is sesed to be busy the ode backs off to a bigger widow with BE =. O a secod busy chael sesig or a collisio the ode backs off to a widow with amaxbe = 5 ad remais costat. If a ode is uable to trasmit its packet withi 5 back-offs the trasmissio is assumed to be a failure ad the packet is dropped. We relax this coditio i this paper ad allow a ode to retrasmit its packet util it is successful. Figure shows the flow chart for a ode usig the IEEE 8.5. MAC. The IEEE 8.5. stadard specifies a data rate of 5 kbps ad a maximum MAC protocol data uit (MPDU) of 7 Bytes. Give this data rate, the trasmissio time for a typical packet of 5 Bytes is 5 time slots ad for the MPDU it is 3 time slots. I [] the the performace of the IEEE 8.5. MAC is evaluated i terms of throughput ad eergy efficiecy usig s simulatios for a maximum of 9 odes. I [] the performace of the stadard MAC is evaluated for medical applicatios where the IEEE 8.5. devices iterface with the traditioal MAC techologies such as Etheret. [5] aalyzes the performace i the cotext of medical body area etworks Fig.. BE = mi(be+, amaxbe) Choose a ew time slot Trasmit. Success? Start: BE = 3 Choose a time slot Wait Time = chose slot? Sese Chael i this time slot. Is it free? Sese Chael i ext time slot. Is it free? Flow chart for IEEE 8.5. operatio at a ode. (BAN) where the eergy efficiecy of body implated sesors is the focus give that their required life time is i the order of -5 years i these applicatios. I [] a queuig aalysis is preseted for the sleep mode with possible fiite buffers. I [3] the performace of the stadard MAC is evaluated i the presece of both uplik ad dowlik traffic i the oe-hop star topology etwork. B. Applicatio Space We cosider the two extremes of the spectrum of oe-hop data collectio applicatios i dese sesor etworks. At oe extreme of this spectrum is cotiuous data collectio ad the other extreme is oe-shot data collectio. Cotiuous Data (CD): I this sceario the sources cotiuously sed data to the sik. We assume that our observatio time is such that all odes always have a packet to sed, i.e., their queues are back-logged. This implies that the etwork reaches steady state ad operates at the saturatio throughput. Performace metrics of iterest i this sceario are the system throughput ad eergy cosumptio. Let Φ CD ad Σ CD be the expected throughput i bps ad expected eergy cosumptio per ode per successful packet trasmissio i Joules respectively. Oe-Shot Data (OSD): I this sceario the sik is iterested i oe-shot data queries such as Which odes have observed the evet? or Which odes have recorded temperatures above 5F?, etc. The respose to such oe-shot queries is a sigle packet from each sesor ode that cotais the locatio of the ode or a similar idetificatio. Oce the packet has bee successfully trasmitted from a ode it is ot i cotetio for the chael aymore, implyig that the system does ot attai steady state. The performace metrics of iterest i this sceario are the delay i obtaiig packets from all sesor odes ad eergy cosumptio icurred by the sesor etwork i this operatio. Let OSD ad Σ OSD be the expected delay i secods ad the amortized expected eergy cosumptio per ode i Joules respectively for successfully trasmittig packets from all sources. Please ote that we are cosiderig the total system throughput ad ot per ode throughput. Per ode throughput ca be calculated by dividig the system throughput by the umber of odes.
I this paper we maily focus o dese sesor etworks i which at-least 5 odes coted for the chael i either sceario. We assume that the packet legths are determiistic ad costat. C. Model Now, we model the IEEE 8.5. MAC as a p-persistet CSMA MAC with chagig p. Before we preset the MAC model, we describe the assumptios made ad the eergy model used. Assumptios: Let the umber of sesor odes i the radio rage of the sik be N. All sesor odes are sychroized to a global time which is divided ito slots of equal legth ad each ode trasmits at the begiig of a time slot. Let the packet legth be L time slots. A sesor ode is iformed of its packets successful trasmissio through ackowledgemet packets (ACKs) from the sik. Failure to receive a ACK from the sik implies a collisio. The ACK is set by the sik as soo as the packet receptio is completed. Table I summarizes the otatios used. Eergy Model: Accordig to the IEEE 8.5. stadard a ode ca exist i ay oe of the followig four states - Shutdow, Idle, Trasmit, Receive. For CD, we assume that the odes are either i the Trasmit or the Recieve state ad are ot cocered with the Shutdow or Idle states. For OSD, agai each ode is either i the Trasmit or the Recieve state util its packet is trasmitted, after which the ode moves to the Shutdow state permaetly. Let the power cosumed i the Trasmit state be ξ T ad the power cosumed i the Recieve state be ξ R. Accordig to [], ξ R = 35 mw ad ξ T = 3 mw for the highest trasmissio power. The power cosumed i the Shutdow state is egligible. MAC Model: I [6] the authors model the IEEE 8.5. MAC i the cotetio access period (CAP) as a o-persistet CSMA with back-off. They approximate the three origial uiform-radom back-off widows to geometrically distributed back-off widows with parameters p, p ad p 3 such that p i = BO i +, ( i 3) where BO i is the origial uiform-radom back-off widow size. With BO = 8, BO = 6 ad BO 3 = 3, the respective values of p, p ad p 3 are.5, 8.5 ad 6.5. I this paper we further simplify this model to a p- persistet CSMA i which the probability of trasmissio chages from p to p to p 3 with each collisio ad remais costat after two collisios at p 3. The key differece i our model from the o-persistet CSMA model is that i our case the trasmissio probability chages with a packet collisio istead of a busy carrier sese. Thus i our model, a ode starts out with a iitial trasmissio probability of p. The ode seses the chael at the begiig of each time slot ad if the chael is foud to be free for two cosecutive time slots, it trasmits its packet with probability p. If the chael is busy, the ode tries to trasmit the packet with the N p L δ ξ R ξ T T E Φ CD (N) Σ CD (N) OSD (N) Σ OSD (N) p T opt (, L) p E opt (, L) Number of odes i the etwork Trasmissio probability Legth of packet i time slots Time slot legth (3 µsecs) Power cosumptio i Receive state Power cosumptio i Trasmit state Number of odes i a epoch Delay i a epoch with odes Eergy cosumptio i a epoch with odes Throughput i bps i CD Eergy cosumptio per ode per successful packet trasmissio i CD Delay i secs to obtai packets from N odes i OSD Eergy cosumptio i Joules to obtai packets from N odes i OSD Trasmissio probability that miimizes epoch delay Trasmissio probability that miimizes epoch eergy cosumptio TABLE I TATION same probability the ext time it fids two cosecutive free time slots. If more tha oe ode trasmits i the same time slot it results i a collisio ad if a ode is ivolved i a collisio for the first time it chages its trasmissio probability to p. O a secod collisio its trasmissio probability is chaged to p 3 ad it remais costat beyod the secod collisio. We evaluate the accuracy of our model usig simulatios. The results are averaged over radom trials with differet radom seeds. For the CD sceario, we simulated the protocol for time slots for a packet legth of 5 Bytes (or 5 time slots). Figure 3 plots the simulatio results comparig the IEEE 8.5. ad our p-persistet CSMA model ad shows that our model is reasoably accurate. Next, we determie the optimal performace of a geeric p-persistet CSMA MAC with a similar time slot structure ad characterize the performace of IEEE 8.5. MAC i compariso to that. III. P-PERSISTENT CSMA MAC I this sectio we model ad aalyze a geeric p-persistet CSMA MAC ad determie the trasmissio probabilities that optimize its performace. A. Overview I a slotted p-persistet CSMA ([]), each ode seses the chael at the begiig of each time slot ad if the chael is foud to be free of ay trasmissios, it trasmits its packet with a probability p. If the chael is ot free, the ode attempts to trasmits its packet i the ext free time slot. If more tha oe ode trasmits i the same time slot it results i a collisio. We have writte our ow simulators i C for the IEEE 8.5. ad p-persistet CSMA MAC protocols. They are available for dowload at http://ceg.usc.edu/ arg/dowloads.html.
Φ CD (N) Kbps Σ CD (N) mjoules 3 5 5 5 p persistet CSMA IEEE 8.5. 5 55 6 65 7 75 8 85 9 95 8 6 p persistet CSMA IEEE 8.5. 5 55 6 65 7 75 8 85 9 95 (a) Cotiuous Data OSD (N) secs Σ OSD (N) mjoules 3 p persistet CSMA IEEE 8.5. 5 55 6 65 7 75 8 85 9 95 8 6 p persistet CSMA IEEE 8.5. 5 55 6 65 7 75 8 85 9 95 (b) Oe-shot Data Fig. 3. IEEE 8.5. stadard is modeled as a p-persistet CSMA with probability of trasmissio reducig i three steps p =.5, p = 8.5, p 3 = with each ew collisio. 6.5 Traditioally, system dyamics due to the p-persistet CSMA protocol have bee modeled usig reewal theory (example [8], [9], [5], []). The key assumptio that makes the use of reewal or regeerative models feasible is that the system attais statioarity ad that the models capture the system behavior at the state. While this assumptio is still true for the CD sceario, it is ot true for the oe-shot data sceario. Nevertheless, we observe the system at every successful packet trasmissio like i [9] ad [5], for both scearios ad derive expressios for throughput, delay ad eergy cosumptio. B. Model We observe the system at every successful packet trasmissio. The time iterval betwee two cosecutive successful trasmissios is defied as a epoch. A epoch is made up of idle time, i which the chael is free of ay trasmissios, collisio time, i which more tha oe ode is trasmittig ad a sigle successful trasmissio time which marks the ed of the epoch, as illustrated i Figure. : Idle Slot : Collisio Slot epoch : Successful Slot Fig.. A epoch illustratig the time iterval betwee cosecutive successful trasmissios. It is importat to ote that, for CD, the umber of odes remai costat i all epochs. However, for OSD the umber of odes decreases by oe with each passig epoch. Let T be the epoch delay the time iterval betwee two cosecutive successful packet trasmissios i secods ad E be the eergy cosumptio the total eergy cosumed by all cotedig odes i Joules, for the epoch with cotedig odes. The Φ CD (N) = (8L) bps () E[T N ] Σ CD (N) = E[E N] N Joules () N OSD (N) = E[T ] secods (3) Σ OSD (N) = N = N E[E ] Joules () = where 8L i Equatio is the packet legth i bits. Clearly, the above metrics are optimized whe E[T ] ad E[E ] are miimized. First we determie expressios for E[T ] ad E[E ]. Propositio : For a costat packet legth L, the expected epoch delay for cotedig odes is give by E[T ] = L (L )( p) p( p) δ (5) Proof: As illustrated i Figure the delay i a epoch is due to idle time, collisio time ad successful trasmissio time. Therefore, the expected delay i epoch, is give by E[T ] = E[T Idle, ] + E[T Collisio, ] + E[T Success ] (6) where E[T Idle, ] is the expected umber of idle time slots, E[T Collisio, ] is the expected umber of collisio time slots ad E[T Success ] is the expected umber of time slots of successful trasmissio. Sice the packet legth L is a costat E[T Success ] is equal to Lδ ad idepedet of. If E[N coll, ] is the expected umber of collisios i a epoch with odes, the E[T Idle, ] = (E[N coll, ] + ) E[T IdleP eriod, ](7) E[T Collisio, ] = E[N coll, ] E[T CollisioP eriod, ] (8)
where E[T IdleP eriod, ] is the expected umber of idle time slots betwee two cosecutive packet trasmissios (collisio or successful) ad E[T CollisioP eriod, ] is the expected umber of collisio time slots at each collisio. Owig to the costat probability of trasmissio p withi a epoch, the IdleP eriods betwee ay two cosecutive packet trasmissios are i.i.d radom variables with the same mea value. Also, sice the decisio to trasmit i a time slot after a free chael sese is idepedet of the umber of previous free chael seses, the umber of collisios is idepedet of the legth of IdleP eriods. This holds true for CollisioP eriods also, thus justifyig the above two equatios. E[N coll, ] ad E[T IdleP eriod, ] are give by [5]: E[N coll, ] = E[T IdleP eriod, ] = ( p) p( p) (9) ( p) ( p) δ () We use the above two equatios to derive the expected delay i the epoch. Sice the packet legth is costat E[T CollisioP eriod, ] = Lδ. Therefore, E[T Idle, ] = p p δ () E[T Collisio, ] = Lδ( ( p) p( p) ) p( p) () Substitutig the above equatios i Equatio 6, we get Equatio 5. Propositio : For a costat packet legth of L, the expected epoch eergy cosumptio for cotedig odes is give by E[E ] = ξ R δ L (L )( p) p( p) + ξ T δ L ( p) (3) Proof: Similar to Equatio 6, the eergy cosumptio i the epoch is equal to the sum of the eergy cosumptio i idle time, the eergy cosumptio i collisio time ad the eergy cosumptio i a successful trasmissio. E[E ] = E[E Idle, ] + E[E Collisio, ] + E[E Success ] () Usig equatios from Propositio, E[E Idle, ] ca be calculated as E[E Idle, ] = (E[N coll, ] + ) ξ R E[T IdleP eriod, (5) ] = ξ R δ p p = ξ Rδ p p (6) Surprisigly, for a costat p, the idle time eergy cosumptio is idepedet of the umber of cotedig odes i a epoch, ad depeds oly o p. Similarly, the collisio time eergy cosumptio is give by E[E Collisio, ] = E[N coll, ] E[E CollisioP eriod, ] (7) The expected eergy cosumptio i a CollisioP eriod, E[E CollisioP eriod, ], is equal to the sum of the expected eergy cosumptio by odes ivolved i packet trasmissios ad the expected eergy cosumptio by odes i idle state durig the CollisioP eriod. Therefore, E[E CollisioP eroid, ] = Lξ T δ +Lξ R δ ip {T ras. = i Collisio} i= ( i)p {T ras. = i Collisio} (8) i= where P {T ras. = i Collisio} is the probability that i ( ) odes trasmit their packets give that a collisio has occurred, ad it is give by P {T ras. = i Collisio} = P {T ras. = i T ras. } ( ) i p i ( p) i = ( p) (9) p( p) Substitutig the above equatio i Equatio 8, we get E[E CollisioP eriod, ] = L(ξ T ξ R )δ p( ( p) ) ( p) p( p) + Lξ R δ () Substitutig the above equatio i Equatio 7, we get E[E Collisio, ] = L(ξ T ξ R )δ ( ( p) ) ( p) + Lξ Rδ ( ( p) p( p) ) p( p) () Ad fially, the expected eergy cosumptio durig a successful trasmissio is give by E[E Success ] = ξ T Lδ + ξ R Lδ ( ) () Substitutig the above equatios i Equatio we get Equatio 3. C. Optimality Let p T opt(, L) ad p E opt(, L) respectively be the trasmissio probabilities at which E[T ] ad E[E ] are miimized. Propositio 3: For >, the trasmissio probability that miimizes the expected epoch delay E[T ] is give by p T opt(, L) =, L = (3) p T + ( )(L ) opt(, L), L > () ( )(L )
Proof: The value of p that miimizes E[T ] is obtaied by equatig its first derivative with respect to p to zero. For L =, de[t ] dp = (5) Optimal p.5.5..35.3.5. T p (,L) opt E p opt (,L), γ = E p (,L), γ = opt E p (,L), γ =.5 opt E p (,L), γ =.5 opt L=5 E[T ] = δ p( p) (6) Takig the derivative ad equatig it to zero results i p =. Similarly, for L >, equatig the derivative of E[T ] from Equatio 5 to zero yields the followig equatio..5..5 Fig. 5. 9 8 7 6 5 3 Number of odes i a epoch () The optimal probability of trasmissio. ( p) = L ( p) (7) L For p <, ( p) ca be approximated to p ( ) p. Usig this approximatio ad further simplificatio, Equatio 7 reduces to Equatio as a uique root to a d E[T ] dp quadratic equatio. It ca be verified that > for p = p T opt(, L), thus miimizig E[T ]. Propositio : For > ad γ = ξ T ξr the trasmissio probability that miimizes the expected epoch eergy cosumptio E[E ] is give by p E + ( )(L ) + L( )(γ ) opt(, L) ( )(L ) + L( )(γ ) (8) Proof: The proof is similar to that of the previous propositio, please refer to [8] for the details. Numerical calculatios show that the approximatios are very close to the actual values. For =, the optimum trasmissio probability is equal, i.e., whe there is a sigle sesor ode left, delay ad eergy are miimized whe it trasmits its packet with probability. Figure 5 plots p T opt(, L) ad p E opt(, L) as a fuctio of the umber of cotedig odes from = to = for differet values of γ. As the figure shows, for optimal performace the probability of trasmissio should icrease with decreasig umber of odes i a epoch i order to avoid excessive idle time slots. We ca also see that the trasmissio probabilities are higher for lower values of γ. This is because if the ode speds more eergy i the Receive state tha i the Trasmit state, eergy is saved if it trasmits more tha it receives. Corollary : If ξ T = ξ R, the p T opt(, L) = p E opt(, L), i.e., the delay ad eergy cosumptio are joitly optimized with a sigle probability of trasmissio for ξ T = ξ R. Proof: For γ = Equatios ad 8 are equal, which proves the corollary. D. Optimality Criteria Now, we discuss some iterestig optimality criteria for the epoch delay ad eergy cosumptio. Propositio 5: Let Γ(L) = (L ) L. If L > ad L is large such that the for optimal trasmissio probability the average epoch delay is a costat equal to Γ(L). p = p T opt(, L) E[T ] Γ(L) (9) Proof: For optimal trasmissio probability, substitutig Equatio 7 ito Equatio 5 we get E[T ] = (L )( pt opt(, L)) p T opt(, L) For large such that, from Equatio (3) p T opt(, L) (3) L p T opt(, L) (3) L Substitutig the above equatios ito Equatio 3 proves the propositio. Corollary : For optimal trasmissio probability ad for large umber of odes such that the throughput of p-persistet CSMA MAC protocol is a costat idepedet of ad depeds oly the legth of the packet. OptimalThrougput L L (L ) packets/timeslot (33) Proof: Throughput is calculated as the iverse of the epoch delay. Equatio 33 is a direct result from Propositio 5. Propositio 6: Let Γ R (L) = L L (L )(. If L > L ) ad is large such that, the for optimal trasmissio probability the ratio of average idle time i a epoch to the average epoch delay is a costat equal to Γ R (L). Also, if the trasmissio probability is greater tha optimal the the ratio is lower tha Γ R (L) ad vice versa. p = p T opt(, L) E[T Idle,] Γ R (L) E[T ] (3) p < (>)p T opt(, L) E[T Idle,] > (<)Γ R (L) E[T ] (35) Proof: Usig Equatios 9, 5 ad 7 for optimal p,
For ( ) E[T Idle, ] = E[T ] L p T opt(, L), usig Equatio L p T opt(, L) L (36) (37) Substitutig the above equatio ito the previous equatio the first part of the propositio is proved. Similarly, for p < (>)p T opt(, L) L p < (>) (38) E[T Idle,] E[T ] L > (<)Γ R (L) (39) Hece the propositio is proved. Figure 6 illustrates Propositio 6 for. The approximatio of the ratio to Γ R (L) is primarily due the approximatio i Equatio. As the figure shows, for low values of the ratio deviates away from Γ R (L). Fig. 6. E[T Idle, ]/E[T ].5.5..35.3.5..5. 9 T p (,L).3 opt T p (,L) opt T p (,L) +.3 opt 8 7 6 5 3 Number of odes i a epoch () Ratio of expected idle time to expected epoch delay. Figure 7 plots the expected delay ad eergy cosumptio for a epoch with = 5 odes as a fuctio of the trasmissio probability p for differet values of the packet legth L. The figure ca be explaied through the followig questio: E[T ] msecs E[E ] mjoules 3 = 5, ξ R = 35 mw, ξ T = 3 mw.5..5..5.3 p 7 6 5 3.5..5..5.3 p L = L = 3 L = L = L = L = 3 L = Fig. 7. Expected delay ad eergy cosumptio i a epoch with odes as a fuctio of trasmissio probability, p, for differet values of packet legth L. L = I p-persistet CSMA, if the legth of the packet is icreased from L to L + l (l > ), should the value of trasmissio probability p be icreased or decreased to maitai the delay ad eergy cosumptio costat? Figure 7 shows us that the aswer to the above questio is that it depeds o the value of p. If p < p T opt(, L), the for the same delay, p should be icreased ad if p > p T opt(, L) the p should be decreased. The same aswer holds true for eergy if p T opt(, L) is replaced by p E opt(, L). The figure also shows that the optimal trasmissio probability values p T opt(, L) ad p E opt(, L) decrease with icreasig L. Figure 8 plots ratios of cosecutive epoch delays ad eergy cosumptios as fuctios of. I this figure, if the ratio is greater tha it implies that the delay or eergy value icreases with decreasig ad vice versa. Greater the differece from higher the rate of icrease or decrease. The followig observatios ca be made from the figure: For p = p T opt(, L), E[T ] is almost costat over all. For p > p T opt(, L), E[T ] shoots up for higher values of due to higher umber of collisios. For p < p T opt(, L), E[T ] shoots up for lower values of due to higher umber of idle time slots. For p = p E opt(, L), E[E ] icreases mootoically with icreasig. For p > p E opt(, L), E[E ] shoots up for higher values of due to higher umber of collisios. For p < p E opt(, L), E[E ] is higher tha the optimal eergy cosumptio values for lower values of due to higher umber of idle time slots. E[T ]/E[T ] E[E ]/E[E ].6...8 L=5, ξ R = 35 mw, ξ T = 3 mw T p = p opt (,L) p =.35 p =..6 3 5 6 7 8 9.9.8.7.6 E p = p (,L) opt p =.35 p =..5 3 5 6 7 8 9 Fig. 8. Ratio of expected delays ad eergy cosumptios for cosecutive epochs. For CD the implicatio of this criterio is that the delay betwee two successful packet trasmissios is idepedet of the umber of odes i the etwork as log as the odes are trasmittig at optimal trasmissio probabilities. For OSD, the implicatio is the followig propositio. Propositio 7: For OSD, if is large such that, the the trasmissio probability is optimal if ad oly if the epoch of delay of two cosecutive epochs are equal. p = p T opt(, L) E[T ] = E[T ] ()
Proof: Please refer to [8] for the proof. IV. CHARACTERIZATION OF IEEE 8.5. Havig determied the performace of optimal p-persistet CSMA, we characterize the performace of IEEE 8.5. MAC i this sectio. Figure 9 plots the average trasmissio probabilities for the IEEE 8.5. MAC (obtaied usig the p-persistet CSMA model) i compariso to the trasmissio probabilities for optimal p-persistet CSMA for both CD ad OSD. The trasmissio probabilities show for IEEE 8.5. are obtaied usig the default values specified i the stadard icludig the two required sesig slots, which is ot required for the geeric p- persistet CSMA MAC. For OSD, the trasmissio probability for IEEE 8.5. quickly stabilizes at 6.5 =.66 ad for CD, close to that value. This behavior is i cotrast to the tred show by optimal probabilities. This implies that the back-off mechaism of IEEE 8.5. protocol ca be modified for optimal performace as follows: The chage of back-off widow sizes should happe at successful trasmissios istead of at collisios or busy chael seses. Further, for OSD, successful packet trasmissios are a better idicator for future cogestio tha collisios or busy chael seses. For CD, the average trasmissio probability for IEEE 8.5. MAC remais almost costat irrespective of the umber of cotedig odes, while for optimal p- persistet CSMA it reduces with N. For optimal performace the widow sizes should be reflective of the umber of cotedig odes. For OSD, the back-off widow size should actually decrease with every successful trasmissio as the optimal trasmissio probability icreases..8.6.. Trasmissio Probabilities, IEEE 8.5. Optimal p persistet CSMA 5 55 6 65 7 75 8 85 9 95..3.. IEEE 8.5. Optimal p persistet CSMA 9 CD OSD, N = 8 7 6 5 3 Number of odes i a epoch () Fig. 9. Compariso of trasmissio probabilities for IEEE 8.5. ad optimal p-persistet CSMA for CD ad OSD. I the ext sectio, we preset a chael feedback ehaced IEEE 8.5. MAC that icorporates the above features. V. ENHANCED IEEE 8.5. The key idea i ehacig the performace of the IEEE 8.5. is to use the optimality criteria for p-persistet CSMA derived i Sectio III. I particular, we cosider the criterio described i Propositio 6 which requires measuremet of the idle time as well as the delay betwee two cosecutive successful trasmissios. These measuremets ca be costrued as feedback from the chael. Before we describe how this feedback ca be used, we review the related work i chael feedback-based medium access cotrol techiques. A. Related Work The idea of usig feedback from the chael to cotrol the trasmissio probabilities of cotedig odes has bee used for a log time. Rivest i [7] has proposed a terary feedback model i which each ode has to moitor three chael coditios - absece of trasmissios, successful trasmissios ad, collisios. Rivest has show that estimatig the true value for the umber of odes ad settig the trasmissio probability to maximizes the throughput i slotted-aloha type protocols (i which the packet legth is equal to a sigle time slot). If the packet legth is of multiple time slots, this results does ot hold true as we have show i Propositio 3 i Sectio III. I [] a cotrol mechaism has bee preseted that uses the eergy cosumed by a tagged ode i the etwork i the above three chael coditios betwee two successful packet trasmissios. This mechaism is ot applicable i the case of OSD because each ode has a sigle successful packet trasmissio. Similar strategies based o the estimatio of the three chael coditios have bee proposed ([], [3], [7]) all of which are more suitable for steady state coditios (like i CD) i which the umber of cotedig odes remai costat. A good cotrol mechaism should deped o the etwork ad traffic coditios as well as the applicatio requiremets. Our objective is to preset a feed-back cotrol mechaism that is suitable for both CD ad OSD scearios. Oe major challege preseted i OSD is to estimate the true system state usig chael coditios i the face of costatly chagig state of the system (decreasig umber of cotedig odes). Nevertheless, the aalysis preseted i Sectio III presets us with uique opportuities to efficietly cotrol the trasmissio probabilities i real time. B. Our Approach Our approach for chael feedback-based cotrol of trasmissio probabilities is maily based o Propositio 6. Accordig to the propositio, if the trasmissio probability is optimal the the ratio of idle time to the delay betwee two cosecutive successful packet trasmissios is Γ R (L). If the trasmissio probability if higher tha the optimal value the the ratio is lower tha Γ R (L) ad vice versa. First we describe how this optimality criterio ca be used for a ehaced p-persistet CSMA ad the adapt it to desig a ehaced IEEE 8.5. MAC protocol. ) Ehaced p-persistet CSMA MAC: Each cotedig ode ca start by choosig a trasmissio probability uiformly at radom i a small iterval of say (,.5). Each ode i the etwork measures the curret epoch s idle time ad delay ad uses these measuremets to determie the trasmissio probability for the ext epoch. If the ratio of
idle time to the delay is lower tha Γ R (L) the it meas that the trasmissio probability would have bee greater tha the optimal value. Therefore the trasmissio probability of the ext epoch should be lower tha the curret epoch s to brig the delay closer to optimal. Similarly, if the ratio if higher tha Γ R (L) the ext epoch s trasmissio probability should be icreased for optimal delay. Thus, the trasmissio probability update rule is give by p ext = p curret α Γ R (L) () where α = T Idle,curret T curret. I this update rule the icrease or decrease i the trasmissio probability is directly proportioal to the value of the ratio α. ) Ehaced IEEE 8.5.: The IEEE 8.5. MAC protocol uses differet widow sizes to cotrol the trasmissio of packets. I order to use the above optimality criterio the trasmissio probability update rule should be coverted ito a widow size update rule. For this we make use of the approximatio we used i Sectio II to model the IEEE 8.5. MAC as a p-persistet CSMA MAC with chagig p. I this, if a uiform-radom back-off widow has a size of W time slots the it ca be closely modeled as a geometric-radom choice of time slot with parameter p as log as p = W +. Thus a trasmissio probability ca be coverted ito widow size by usig the iverse relatioship, i.e., W = p p. Based o this ad the trasmissio probability update rule give above, the widow update rule for the Ehaced IEEE 8.5. MAC is: W ext = (W curret + )Γ R (L) α () α A key aspect of this update rule is that, all odes i the etwork should updated their widows at every successful packet trasmissio. Figure shows the flow chart for the Ehaced IEEE 8.5. MAC operatio at a ode. Fig.. Start p = rad(,.5) W = (-p)/p Choose a time slot Wait Time = chose timeslot? Sese Chael i this time slot. Is it free? Chage Widow Size W ext = ((W curret + ) R (L) ) / Choose a ew time slot Sese Chael i ext time slot. Is it free? From Chael: Is there a successful trasmissio? Do t Chage Widow Choose a ew time slot Trasmit. Success? Flow chart for Ehaced IEEE 8.5. operatio at a ode. It should be oted that all aspects of the origial IEEE 8.5. MAC have bee preserved except for whe the widow is chaged ad how it is chaged. 3) Evaluatio: Figure shows the performace gais for the Ehaced IEEE 8.5. MAC i compariso to the origial. The figure also shows the performace of the optimal p-persistet CSMA ad ehaced p-persistet CSMA. It should be oted that the performace of the ehaced IEEE 8.5. MAC matches that of the ehaced p-persistet CSMA MAC for CW =, i.e., if the odes do ot sese the chael for two cosecutive free slots but trasmit their packet oce their chose time slot occurs. Thus, for the ehacemet we use, the performace of the ehaced p-persistet CSMA is a upper-boud o the performace of the ehaced IEEE 8.5. MAC. A importat observatio from the figure is that the system throughput reduces drastically with icreasig umber of cotedig odes for the origial IEEE 8.5. MAC. But for the ehaced versio, the system throughput is almost costat with the umber of odes. Implyig that it is much more scalable tha the origial. This holds for eergy also. These sigificat gais i performace are observed for both CD ad OSD scearios. ) Discussio: I actual implemetatio the measuremet of idle time ad the delay betwee two cosecutive successful packet trasmissios ca be achieved easily at each ode by observig ACKs from the sik. If all odes i the etwork are i the radio rage of each other the all odes see the same idle time betwee two cosecutive successful packet trasmissios. If o the other had, all odes are i the radio rage of the sik but ot i the radio rage of each other the each ode sees a idle time that is based o the umber of odes i its eighborhood. Thus, the above update rule tries to optimize the trasmissio probability for the umber of odes i the eighborhood of each ode ad ot for the etire etwork. However, the sik ca measure the idle time for the etire etwork ad piggy back this value i the ACKs to the sesor odes. The sesor odes measure the epoch delay as the iterval betwee the ACKs. Thus, i this case, the chael feedback is via the sik. The performace differece i terms of degradatio or improvemet, if ay, betwee the local feedback ad global feedback based mechaisms eeds to be ivestigated. This will be oe of the directios for our future work. A importat aspect of the Ehaced IEEE 8.5. MAC protocol is that all odes should chage their widow sizes ad choose a ew time slot (or start a ew couter) at every successful packet trasmissio. Otherwise, oly a few odes optimize their widow sizes ad this could lead to ufairess i the CD sceario. Aother importat aspect to cosider is the effect of chael errors. The curret stadard MAC assumes chael errors based packet losses to be collisios ad backs-off accordigly, thus miscostruig chael errors as cogestio. But the ehaced MAC protocol does ot chage ay protocol parameters due to chael errors based packet losses, as successful packet trasmissios are take as the oly idicators of chael cogestio. Nevertheless, a thorough ivestigatio of the effect of chael errors will be a importat part of our
Φ CD (N) Kbps 5 5 OSD (N) secs 3 IEEE 8.5. Optimal p persistet CSMA Ehaced p persistet CSMA Ehaced IEEE 8.5. Σ CD (N) mjoules 5 55 6 65 7 75 8 85 9 95 8 6 IEEE 8.5. Optimal p persistet CSMA Ehaced p persistet CSMA Ehaced IEEE 8.5. 5 55 6 65 7 75 8 85 9 95 (a) Cotiuous Data Σ OSD (N) mjoules 5 55 6 65 7 75 8 85 9 95 8 6 IEEE 8.5. Optimal p persistet CSMA Ehaced p persistet CSMA Ehaced IEEE 8.5. 5 55 6 65 7 75 8 85 9 95 (b) Oe-Shot Data Fig.. Performace of Chael Feedback Ehaced IEEE 8.5.. future work. I this paper we have focused o dese sesor etworks. The followig table shows the throughput performace compariso of the origial ad ehaced IEEE 8.5. MAC protocols for lower umber of odes. Clearly, accordig to the results, the curret MAC performs better tha the ehaced MAC for low umber of odes. But with icreasig umber of odes, the ehaced MAC icreasigly performs better. N 3 Origial 85 58.75 38.75 Ehaced 3.75 63.75 63.75 6 TABLE II PERFORMANCE COMPARISON OF ORIGINAL AND ENHANCED IEEE 8.5. MAC FOR CD IN TERM OF THROUGHPUT (Φ CD (N)) IN KBPS FOR Low DENSITY NETWORKS. I the ehaced MAC protocol we have used a sigle optimality criterio from Sectio III. We would like to ivestigate the use of the other criteria also. Recet research has focused o the effect of capture effect o wireless MAC protocols. I the future we wish to study the ifluece of capture effect o the ehaced IEEE 8.5. MAC for the two data collectio scearios. I additio, a thorough simulatio study of the ehaced protocol will be part of our future work. VI. CONCLUSION We have show that the curret IEEE 8.5. MAC performs poorly for data collectio i dese sesor etworks. We preseted a chael feedback ehaced MAC protocol that performs sigificatly better tha the curret versio. For this we modeled the IEEE 8.5. MAC as a p-persistet CSMA with chagig p, optimized a geeric p-persistet CSMA MAC ad used the resulatat optimality criteria to propose a chael feedback-based ehacemet for the origial IEEE 8.5. MAC. Results showed that our Ehaced IEEE 8.5. MAC scales sigificatly better for both cotiuous data ad oeshot data collectio scearios i dese etworks (umber of odes is greater tha 5). For low desity etworks the performace of the curret MAC is better for upto 5 odes after which the performace of the ehaced MAC is better. REFERENCES [] http://www.chipco.com/files/cc Data Sheet 3.pdf. [] D. Bertsekas ad R. Gallager. Data Networks (Secod Editio). Pretice Hall, 99. [3] B.Hajek ad T. Loo. Decetralized Dyamic Cotrol of a Multi-Access Broadcast Chael. IEEE Trasactios o Automatic Cotrol, 7:559 569, 98. [] R. Bruo, M. Coti, ad E. Gregori. Optimizatio of Efficiecy ad Eergy Cosumptio i p-persistet CSMA-Based Wireless LANs. IEEE Trasactios o Mobile Computig, (): 3, Jauary March. [5] F. Cali, M. Coti, ad E. Gregori. Dyamic Tuig of the IEEE 8. Protocol to Achieve a Theoretical Throughput Limit. IEEE/ACM Trasactios o Networkig, 8(6):785 799, December. [6] E. Callaway, P. Gorday, L. Hester, J. A. Gutierrez, M. Naeve, B. Heile, ad V. Bahl. Home Networkig with IEEE 8.5.: A Developig Stadard for Low-Rate Wireless Persoal Area Networks. IEEE Commuicatios Magazie, pages 7 77, August. [7] F. Kelly. Stochastic Models of Computer Commuicatios Systems. Joural of Royal Statistical Society, Series B, 7:379 395, 985. [8] L. Kleirock ad F. A. Tobagi. Packet switchig i radio chaels: Part i carrier sese multiple access modes ad their throughput-delay characteristics. IEEE Trasactios o Commuicatios, 3: 6, December 975. [9] S. S. Lam. Carrier Sese Multiple Access Protocol for local etworks. The Iteratioal Joural of Distributed Iformatique, : 3, 98. [] G. Lu, B. Krishamachari, ad C. S. Raghavedra. Performace Evaluatio of the IEEE 8.5. MAC for Low-rate Low-Power Wireless Networks. I IEEE IPCCC, pages 7 76, April. [] M.Gerla ad L.Kleirock. Closed Loop Stability Cotrol for S-Aloha Satellite Commuicatios. pages 9, September 977. [] J. Misic, V. B. Misic, ad S. Shafi. Performace of IEEE 8.5. beaco eabled PAN with uplik trasmissios i o-saturatio mode - access delay for fiite buffers. I IEEE BroadNets, October. [3] J. Misic, S. Shafi, ad V. B. Misic. Performace of a Beaco Eabled IEEE 8.5. Cluster with Dowlik ad Uplik Traffic. IEEE Trasactios o Parallel ad Distributed Systems, 7():36 376, 6. [] D. C. N. Golmie ad O.Rebala. Performace Aalysis of Low Rate Wireless Techologies for Medical Applicatios. I Compuer Commuicatios (Elsevier), pages 8:66 75, Jue 5. [5] N.F.Timmos ad W.G.Scalo. Aalysis of the Performace of IEEE 8.5. for Medical Sesor Body Area Networkig. I IEEE SECON, pages 6,. [6] I. Ramachadra, A. K. Das, ad S. Roy. Aalysis of the Cotetio Access Period of IEEE 8.5. MAC. Accepted for publicatio i ACM Trasactios o Sesor Networks., September 5. [7] R.L.Rivest. Network Cotrol by Bayesia Broadcast. IEEE Trasactios o Iformatio Theory, 33(3), 987. [8] Kira Yedavalli, Bhaskar Krishamachari. Ehacemet of the IEEE 8.5. MAC Protocol for Scalable Data Collectio i Dese Sesor Networks. USC Techical Report CENG-6-, November 6.