Research Article Delay Analysis of GTS Bridging between IEEE and IEEE Networks for Healthcare Applications

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1 Hidawi Publishig Corporatio Iteratioal Joural of Telemedicie ad Applicatios Volume 29, Article ID 98746, 13 pages doi:1.1155/29/98746 Research Article Delay Aalysis of GTS Bridgig betwee IEEE ad IEEE Networks for Healthcare Applicatios Jelea Mišić 1 ad Xuemi Sherma) She 2 1 Departmet of Computer Sciece, Uiversity of Maitoba, Wiipeg, MB, Caada R3T 2N2 2 Departmet of Electrical ad Computer Egieerig, Uiversity of Waterloo, Waterloo, ON, Caada N2L 3G1 Correspodece should be addressed to Jelea Mišić, jmisic@cs.umaitoba.ca Received 16 Jue 28; Accepted 18 September 28 Recommeded by Yag Xiao We cosider itercoectio of IEEE beaco-eabled etwork cluster with IEEE 82.11b etwork. This sceario is importat i healthcare applicatios where IEEE odes comprise patiet s body area etwork BAN) ad are ivolved i sesig some health-related data. BAN odes have very short commuicatio rage i order to avoid harmig patiet s health ad save eergy. Sesed data eeds to be trasmitted to a access poit i the ward room usig wireless techology with higher trasmissio rage ad rate such as IEEE 82.11b. We model the itercoected etwork where IEEE based BAN operates i guarateed time slot GTS) mode, ad IEEE 82.11b part of the bridge coveys GTS superframe to the 82.11b access poit. We the aalyze the etwork delays. Performace aalysis is performed usig EKG traffic from cotiuous telemetry, ad we discuss the delays of commuicatio due the icreasig umber of patiets. Copyright 29 J. Mišić ad X. Sherma) She. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. 1. Itroductio Wireless sesor etworks i healthcare applicatios require small lightweight devices with sesig, computatioal, ad commuicatio features to be uobtrusively placed o patiet s body. They eed to commuicate results of sesig of healthcare data periodically over very short rage to the devices which ca be carried by the patiet or mouted o patiet s bed. We refer to the wireless sesor etwork o patiet s body as body area etwork BAN). Low power, that is, short commuicatio rage of wireless sesors is eeded for health, iterferece, ad security reasos. Devices which collect the results of measuremets eed to provide some limited data processig ad aggregatio, add security/privacy fuctios, ad commuicate aggregated data to the LAN access poit i patiet s ward room as show i Figure 1. We refer to this device as bridge. I this paper, we cosider itercoectio of IEEE beaco-eabled etwork cluster with IEEE 82.11b etwork. The IEEE odes comprise patiet s body area etwork BAN) ad are ivolved i sesig some healthrelated data which will be trasmitted to the access poit i the ward room usig wireless techology such as IEEE 82.11b. It is clear that the etwork performace depeds o the characteristics of the itercoectio device. Therefore, we model the itercoected etwork where IEEE based BAN operates i guarateed time slot GTS) mode, ad IEEE 82.11b part of the bridge coveys GTS superframe to the 82.11b access poit. We the aalyze the impact of importat parameters such as acceptable load rages ad the delays of commuicatio due the icreasig umber of patiets. Sice real-time operatio of the bridges is ecessary for may measuremets i hospitals besides itesive care uits ICUs), we will study commuicatios through the bridge for simple case of EKG cotiuous telemetry. The remaider of the paper is orgaized as follows. We review the etworkig aspect of healthcare wireless sesor etworks with the emphasis o cotiuous electrocardiogram telemetry i Sectio 2. ISectio 3, wereview the properties of beaco-eabled MAC ad IEEE 82.11b MAC related to the operatio of bridge. I Sectio 4, we preset the cocepts of bridge desig betwee IEEE BAN ad IEEE 82.11b ward LAN. Aalytical model of bridge where BAN operates i GTS mode is preseted

2 2 Iteratioal Joural of Telemedicie ad Applicatios i Sectio 5. I Sectio 6, we preset performace results for itercoected clusters uder various modes of bridge access. Fially, Sectio 7 cocludes the paper. 2. Wireless Sesor Networks for Healthcare I today s hospitals, there is a urget eed for timely moitorig the health status of may patiets, especially those with respiratory ad cardiac problems. The eed for cotiuous fetal heart rate moitorig as well as moitorig for movemets of patiets suffered from stroke or Parkiso s disease is also high. Although these applicatios require differet kids of sesors to measure levels of oxyge i blood, heart rate, or motio of body parts, there is uified eed for sesors to be uobtrusively attached to the patiet s body ad for measured data to be trasmitted i a reliable ad secure way i order to be recorded o moitorig devices i real time. Most of the health variables are periodic ad have to be periodically sampled ad digitized. The samplig period has to be at least twice as large as the highest frequecy of the healthcare variables. Recetly, several medical telemetry applicatios have bee prototyped so far ad moved to productio phase such as pulse oximeters, EKG devices, ad motio aalysis systems [1]. Wireless trasmissio is curretly implemeted usig Bluetooth IEEE ad IEEE 82.11b techologies although IEEE emerges as most suitable for medical applicatios due to its low-power ad lowbadwidth requiremets. Some iitial work i this area has bee reported i [1 4]. However, curret reports o wireless healthcare products are focused o reliable hardware ad software desigs of sesor modules while the wireless trasmissio has bee cosidered i testig phase ad for sigle device oly. There is a area of research ivolvig coordiatio ad real-time trasmissio of large umber of healthcare measuremets, which has ot attracted sufficiet attetio. I this paper, we will address the followig problems. 1) Itercoectio of low-power IEEE motes which are coveiet for attachmet o patiet s body) with IEEE 82.11b etwork which has larger badwidth ad larger trasmissio rage. We will desig bridge betwee IEEE wireless commuicatio iterfaces) residig at patiet s body ad IEEE 82.11b residig at bedside or carried i patiet s pocket. More specifically, we will use TDMA feature of IEEE called guarateed time slots to fill it with digitized samples ad pass it to the iterface of IEEE 82.11b for further trasmissio to the hospital room s access poit. 2) Aalysis of delay of real-time health measuremet data icurred by trasmissio techologies. We will use measuremet data for electrocardiogram ad aalyze traffic whe the umber of patiets icreases. Security is aother importat issue i wireless healthcare sesor etworks. I this paper, we will also address data itegrity issue by assumig that there is a shared secret key Patiet s body area etwork Room or ward Room/ward WLAN access poit Body area etwork coordiator ad bridge to room/ward WLAN Room/ward etwork wired) Patiet sesor odes Figure 1: Networkig structure of the ward room with BANs, bridges, ad ward LAN. betwee sesor mote ad bridge device. Secret key will be used to provide message autheticatio code i each superframe packet) usig HMAC fuctio [5, 6] EKG Measuremet. Electrocardiogram ECG or EKG) is a surface measuremet of the electrical potetial geerated by the electrical activity, which cotrols pumpig actio of cardiac muscle fibers. These electrical impulses geerate voltage, which further geerates curret flow i the torso ad potetial differeces o the ski. Stadard EKG moitorig ivolves short-term 3 secods) moitorig of heart pulses usig 12 ski electrodes called leads) placed at desigated locatios o the patiet s body icludig chest, arms, ad legs. Each pair of leads measures voltage which gives oe aspect of the heart s activity. A EKG picture produced by 12 leads allows diagosis of wide rage of heart problems. However, this measuremet is short-term ad requires wired coectio betwee the patiet ad electrocardiograph. I may cases, however, it is ecessary to have cotiuous ad tetherless measuremets of heart rate. For such applicatio, oly three leads placed at patiet s upper ad lower chest ca trace a wide rage of cardiac arrhythmias. Oe ode of these three collects sigals, amplifies the sigal differece, samples the amplified aalog sigal, ad digitizes it. Stadard cliical EKG applicatio has the badwidth of.5 Hz to 1 Hz. For pacemaker detectio, upper frequecy ca be up to 1 khz. There are may desig issues out of scope of this work related to oise suppressio ad filterig frequecies from power lie ad respiratio. I this paper, we assume that upper frequecy of the EKG sigal is 1 Hz. EKG sigal is sampled with 2 Hz, ad each sample is digitized with 12 bits [3]. Therefore, basic badwidth of EKG sigal i stadard cotiuous telemetry is oly 24 bps. 3. Basic Properties of IEEE Std ad IEEE 82.11b MACs 3.1. Basic Properties of IEEE Std MAC. I beacoeabled etworks, the persoal area etwork PAN) coordiator divides its chael time ito superframes [7]. Each superframe begis with the trasmissio of a etwork beaco, followed by a active portio ad a optioal iactive

3 Iteratioal Joural of Telemedicie ad Applicatios 3 Beaco Cotetio-access period CAP) Cotetio-free period CFP) Beaco Guarateed time slot GTS GTS) Iactive Superframe duratio SD) Beaco iterval BI) Figure 2: The compositio of the superframe uder IEEE Std adopted from [7]). portio, as show i Figure 2. The coordiator iteracts with its PAN durig the active portio of the superframe, ad may eter a low-power mode durig the iactive portio. Raw data rate i idustrial, scietific, ad m edical ISM) bad is 25 Kbps. Basic time uit i the stadard is backoff period which cotais 1 bytes. Duratio of active ad iactive parts of the superframe is regulated with MAC parameters SO =,..., 14 which is kow as macsuperframeorder ad BO =,..., 14, also called macbeacoorder. Active superframe part is divided ito 16 slots. Each slot cosists of 3 2 SO backoff periods, which gives the shortest active superframe duratio abasesuperframeduratio of 48 backoff periods whe SO =. Duratio of a active superframe part is deoted as SD = abasesuperframeduratio 2 SO superframe duratio). The time iterval betwee successive beacosisequaltobi = abasesuperframeduratio 2 BO. The duratio of the iactive period of the superframe ca be determied as I = abasesuperframeduratio 2 BO 2 SO ). Period betwee the beacos is equal to the active superframe duratio oly if there is o iactive period i the cluster time, ad, otherwise, it is larger tha active superframe part, that is, BO SO. A active superframe part cosists of cotetio part ad TDMA, that is, guarateed time slot GTS) part. GTS badwidth must be requested by the ode usig the MAC commad frame. Coordiator allocates the GTS badwidth i multiples of slots. Oe slot cotais 3 2 SO backoff periods. Data trasfer from a ode to PAN coordiator ca be doe i GTS slots or usig slotted CSMA-CA access described below. Slotted CSMA-CA algorithm cosists of backoff activity, two clear chael assessmets CCAs), packet trasmissio, ad optioally receipt of the ackowledgmet. Backoff value is uiformly chose i the rage, w 15 1) which is called cotetio widow. Durig backoff coutdow ode does ot liste to the medium, ad checks the activity o the medium oly twice whe backoff cout is fiished. By default, the ode ca have m = 5 trasmissio attempts with backoff widow sizes W 15, = 8W 15,1 = 16, W 15,2 = 32, W 15,3 = 32, ad W 15,4 = 32. To avoid cofusio, we will use subscript 15 to label MAC parameters which have their couterparts i the IEEE 82.11b stadard Basic Properties of IEEE 82.11b Needed for Bridgig. IEEE has much more sophisticated CSMA-CA scheme at the MAC layer. I this protocol opposite to IEEE ), a statio havig a packet to trasmit must iitially liste to the chael to check if aother statio is trasmittig. If there is o trasmissio i distributed iterframe space DIFS) time iterval, the trasmissio ca proceed. If medium is busy, the statio has to wait util curret trasmissio has fiished. The, statio will wait for DIFime period ad the geerate a radom backoff time before trasmittig its frame. This backoff time is uiformly chose i the rage, w 11 1). Backoff couter will be decremeted after each slot time give that trasmissio medium is free, otherwise, its value will be froze util medium becomes free agai for DIFime uits slot time is derived from the propagatio delay time to switch from receivig to trasmittig mode ad time to pass the iformatio about the physical chael state to MAC layer. It actually correspods to backoff period from IEEE ). Statio will trasmit whe its backoff couter reaches zero value. Whe the packet is received, receiver replies with ackowledgmet ACK) packet after short iterframe space SIFS) time iterval. Wheever packet collisio occurs, ackowledgmet will ot be received withi SIFS + ACK time, ad trasmissio has to be reattempted with doubled cotetio widow. If startig widow size is w 11 = W 11,mi after m 11 retrasmissios, its maximal value will become W 11,max = 2 m11 W 11,mi i order to distiguish betwee similar variables i two stadards, we use subscript 11). I our model, we assume that if packet experieces more tha m 11 collisios, last backoff stage will be etered for every subsequet retrasmissio util frame is successfully trasmitted. I order to limit packet collisio time, ad guard agaist hidde termial problem, the stadard allows small reservatio packets request to sed RTS) ad clear to sed CTS) set usig CSMA-CA. After trasmissio of RTS packet, receiver replies with CTS after short iterframe spacesifs) time. Due to sesitivity of healthcare applicatios, we will assume that RTS/CTS scheme is used to protect packets with measuremet data of health variables. The IEEE 82.11b stadard is mostly deployed i curret implemetatios of healthcare wireless sesor etworks [1]. The IEEE 82.11b has higher-speed physical layer tha origial IEEE ad allows trasmissios at 1, 2, 5.5, ad 11 Mbps, while IEEE supports trasmissio at 2 Mbps. However, physical layer header is trasmitted at 1 Mbps, MAC layer header ad payload ca be trasmitted

4 4 Iteratioal Joural of Telemedicie ad Applicatios k k = 1) k k = 78) k k = 15) 24 MHz MHz Figure 3: Used spectra of wireless LAN ad PAN techologies i ISM bad. at 1, 2, 5.5, or 11 Mbps while cotrol frames RTS, CTS, ad ACK are trasmitted at 1 or 2 Mbps. It is also worth otig that sice IEEE 82.11b adapters trasmit at a costat power, distaces covered with trasmissio speeds of 1, 2, 5.5, ad 11 Mbps are 12, 9, 7, ad 3 m, respectively [8]. Startig with semial work i [9], performace of IEEE has bee extesively studied first for saturated case ad later for usaturated case [1 13]. Stadard extesio IEEE 82.11e ehaces CSMA-CA access by itroducig differet iterframe spaces ad differet backoff widow rages for differet traffic classes. This scheme has bee modeled usig similar approach although more complex) as basic scheme i [14 16]. However, give the fact that all BANs have the same priority ad short packet sizes with sesig iformatio, we believe that IEEE 82.11b ca serve the purpose ad that deploymet of IEEE 82.11e at this poit may ot be ecessary. 4. GTS Bridge Desig Bridge cosists of IEEE PAN coordiator ad ordiary IEEE 82.11b iterface. These two compoets are itercoected through a buffer which is filled by the PAN coordiator ad emptied by IEEE 82.11b packet trasmissio facility. IEEE PAN coordiator iterface ad IEEE 82.11b iterface have their wireless trasmit/receive ateas. Both etworks operate i ISM bad as show i Figure 3, ad there is a eed to coordiate operatio of bridge s iterfaces either i TDMA or FDMA maer. From Figure 2 ad discussio i Sectio 3.1, we observe that it is possible to achieve TDMA coordiatio betwee the iterfaces usig the fact that WLAN bridge iterface ca operate durig silet BAN periods. However, i the presece of multiple BANs withi WLAN coverage, this approach requires sychroizatio of BAN beacos we assume that iterferece amog BANs is avoided by separatio i space or by allocatig separate chaels as show i Figure 3). Also badwidth allocatio through SO ad BO parameters must be achieved such that bridged traffic fromallbanscabe delivered durig commo) iactive superframe part. It is much more coveiet if operatio of BAN ad WLAN is separated i frequecy domai because BAN beacos do ot eed to be sychroized ad more badwidth is allocated to the bridge. BAN chaels should be chose i such way that they do ot overlap with ward WLAN chael. From Figure 3, we see that each WLAN chael overlaps with four BAN chaels. Therefore, for each ward WLAN chael, 12 out of 16 BAN chaels should be used i order to avoid iterferece. Duratio of beaco iterval BI is tued accordig to period of sesed health variable. Duratio of active period SD is chose i order to 1) achieve data trasmissio with high success probability i the case of CSMA-CA MAC, 2) i case of GTrasmissio of sesed data, GTS badwidth has to match ecessary size of a group of GTS packets ad ackowledgmet laes where group size correspods to the umber of IEEE odes i BAN. However, some small cotetio periods must be reserved i the superframe i order to commuicate commad frames betwee sesig odes ad PAN coordiator. Sice badwidth of IEEE 82.11b is much larger tha the badwidth of IEEE BAN, trasmissio of oe IEEE 82.11b packet will take short time, ad rest of active period ca be used to exchage some commad data betwee the bridge ad access poit of the ward room. Betwee two trasmissio phases, sesig odes ad bridge are idle ad ca turoff their trasmitters ad receivers. Duratio of this sleep time is BI SD. We make a importat remark about time scales i IEEE ad IEEE 82.11b. Duratio of backoff period i is 32 microsecods, ad with raw data rate of 25 Kbps, oe backoff period carries 1 bytes of data. IEEE slot duratio is 3 2 SO backoff periods. O the other had, IEEE 82.11b backoff couter is decremeted after slot time which is equal to 2 microsecods. Therefore, time-scale traslatio is eeded betwee two etworks. We assume that traffic itesity due to sesig of health variables i BAN will be light give that the umber of odes is lower tha 16, ad that offered load per ode is lower tha few Kbps. This is well below the rate of 25 Kbps supported by IEEE Bridge s buffer will be served by IEEE 82.11b CSMA- CA MAC for which the Markov chai model is preseted i Figure 4. I our modelig, we will assume that data buffers at BAN odes ad at the bridge are ifiite. Although, this assumptio may appear urealistic for sesor odes ad we have always modeled small fiite buffers i our work [17]); offered load to the ode is low so that ode s buffer is empty most of the time. Therefore, both the queuig model with fiite ad ifiite buffers will give similar results. Give the lower computatioal complexity of the model with ifiite buffer, we use it i our aalysis although use of fiite buffer model is straightforward. Assumptio of ifiite buffer at

5 Iteratioal Joural of Telemedicie ad Applicatios 5 1 φ 11 φ 11 idle) φ 11 /W φ 11 /W φ 11 /W φ 11 /W 1 P b 1 P b 1 P b γ 11 π 11,, W 1,W 2, 1, P bs P bs P bs 1 γ 11 γ 11 1 π 11, ) C P t bc P bc P bc 1 γ 11 )/W 1 1 γ 11 )/W 1 1 γ 11 )/W 1 1 γ 11 )/W 1 1 P b 1 P b 1 P b γ 11 π 11, 1, W 1 1 1,W 1 2 1,1 1, P bs P bs P bs 1 γ 11 γ 11 1 π 11, ) C P t bc P bc P bc 1 γ 11 )/W i 1 γ 11 )/W i 1 γ 11 )/W i 1 γ 11 )/W i 1 P b 1 P b 1 P b γ 11 π i, W 11, i 1 i, W i 2 i,1 i, S P t bs P bs P bs 1 γ 11 γ 11 1 π 11, ) P bc P bc P bc 1 γ 11 )/W m,11 1 γ 11 )/W m,11 1 γ 11 )/W m,11 1 γ 11 )/W m,11 1 P b 1 P b 1 Pb γ 11 π 11, m 11, W m 1 m 11, W m 2 m 11,1 m 11, 1 γ γ 11 1 π 11, ) S 11 P t bs P bs P bs C P t bc P bc P bc 1 γ 11 )/W m,11 1 γ 11 )/W m,11 1 γ 11 )/W m,11 1 γ 11 )/W m,11 Figure 4: Markov chai for IEEE 82.11b coupled with device s queue. the bridge is reasoable sice it may cotai more complex hardware ad software, ad offeredload per bridge is low-tomoderate, depedig o the umber of patiets i viciity of access poit. 5. Aalytical Model of GTS Bridgig I geeral case of GTS, bridge sesors may report differet medical variables, such as heart rate, level of oxyge i blood, ad temperature. Each sesor is allocated a umber of slots i uplik directio to carry uplik sesig data ad a slot i dowlik directio to carry ackowledgmet. We will refer to the umber of slots i uplik directio as packet lae. PAN coordiator receives data from statios i separate GTS packet laes, geerates ackowledgmets, ad passes aggregated packets to IEEE 82.11b buffer. Assume that each sesor eeds to be served with data rate D s bps. This results i allocatio of d s packet laes such

6 6 Iteratioal Joural of Telemedicie ad Applicatios Table 1: Compariso of MAC parameters betwee beaco-eabled IEEE ad IEEE 82.11b. CSMA-CA parameter IEEE IEEE 82.11b Backoff period size 32 μs 2μs Liste to the medium durig backoff cout o yes Freeze the backoff ctr. whe medium is busy o yes Liste to the medium immediately before the tras. yes o Actio whe medium is sesed busy New backoff phase Freeze the backoff ctr. Typical size of miimum backoff widow 8 32 Typical umber of backoff phases m 5 5 Raw data rate 25 Kbps 1, 2, 5.5 or 11 Mbps Typical physical + MAC layer header size bits bits RTS ad CTS No i beaco eabled versio Yes that D s = d s 3 2 SO BO.32, 1) ad that period betwee the beacos BI= 48 2 BO.32 matches the samplig period of health variable. Assumig that there are 15 < 16 sesors i the BAN, each sesor will have oe GTS slot, ad the last slot will cotai aggregated ackowledgmets for all sesors. For larger umber of sesors where 15k 1) < 15 15k period betwee the beacos has to be decreased k times, such that each superframe carries readigs from at most 15 sesors ad ackowledgmets i the last GTS slot). For simplicity, let 15 < 16 ad the payload of the IEEE superframe becomes payload of IEEE 82.11b frame cosistig of 15 d s 3 2 SO 1 bytes. IEEE 82.11b frame legth i bytes has to be augmeted with headers from physical ad MAC 82.11b layer which is 5 bytes. Fially, we have to fid frame size i 82.11b slots backoff periods), sice each slot carries umber of bits s 11 equal to the product of raw data rate ad slot duratio, ad its value is equal to l 11 = d s 3 2 SO 1)/s 11. Duratio of RTS, CTS, ad ACK frames expressed i slots will be deoted as rts, cts, adack 11,respectivelywewill use subscript 11 to deote IEEE 82.11b wheever potetial ambiguity may arise betwee two stadards). Duratio of DIFS ad SIFS periods i slots will be deoted as difs ad sifs. Probability geeratig fuctio PGF) for the successful packet trasmissio time is equal to [12] Stz) = z rts+cts+l11+3sifs+difs+ack11, 2) with average value St = St 1) = rts + cts + l 11 +3sifs + difs + ack 11. I the case of collisio of RTS packets activity o medium has PGF: Ctz) = z rts+cts+sifs+difs, 3) with average value Ct = Ct 1) = rts + cts + sifs + difs. Assume that there are 11 bridges attached to the IEEE 82.11b access poit. Each bridge commuicates the same kid of sesig traffic towards the access poit. Usig the assumptio from previous work [2 5, 9, 14, 15] that probability of successful trasmissio is idepedet of the backoff stage,wewilldeoteitasγ 11 while collisio probability is 1 γ 11. Access probability is also idepedet of the backoff stage ad is deoted as τ 11. Relatioship betwee these two probabilities is γ 11 = 1 τ 11 ) 11 1). 4) Probability that medium will be active durig the backoff coutdow of oe statio has two compoets. First oe is the probability that statio sesed the medium busy due to successful trasmissio of oe amog 11 1 statios, ad it has the value p bs = 11 1)τ 11 1 τ 11 ) 11 2).The other compoet is the probability that statio seses the medium busy due to collisio amog some of 11 2 other statios ad has the value p bc = 1 1 τ 11 ) 11 1) p bs. Their sum is the probability that medium is busy durig the backoff coutdow, ad that backoff couter is froze p b = p bs + p bc = 1 γ 11. The PGF for the duratio of time betwee two successive backoff coutdows is represeted with the followig equatio [12]: Hdz) = zγ 11 + p bc Ctz)+p bs Stz) ) Hdz). 5) At this poit, we ote that duratio of period betwee two successive decremets of backoff couter is limited to the maximum packet size. After trasmissio is fiished ad DIFS period passes ay statio doig the backoff,coutdow has to decremet its backoff couter at least oce before packet trasmissio: W 11,i 1 B 11,i z) = k= 1 W 11,i H k d z) = HW11,i d z) 1 W 11,i Hd z) 1 ), 6) where W 11,i = 2 i W 11, for i m 11,adW 11,i = 2 m11 W 11, for i>m 11.

7 Iteratioal Joural of Telemedicie ad Applicatios 7 Assumig that packet will be retrasmitted util valid ackowledgemet is received, the PGF for the packet service time becomes T 11 z) = m 11+1 i 1 i=1 j= m11 + j= B 11,j z)) 1 γ11 ) i 1)Ctz) i 1) γ 11 Stz) ) B 11,j z) i=m 11+1 B11,m11 z) ) i m 11) 1 γ 11 ) i 1)Ctz) i 1) γ 11 Stz), ad its average value is obtaied as T 11 = T 111) Markov Chai Model ad Queuig Model for the GTS Bridge s Output. I the derivatios above, we have derived probability of successful trasmissio ad probability of freezig the backoff period usig the variable which represeted access probability per 82.11b slot τ 11. Access probability, o the other had, has to be derived usig two modelig compoets. First oe is the Markov chai which represets coditioal activities withi the CSMA- CA process. Secod compoet idicates the probability that bridge will be idle ad that it will ot perform backoff cout ad attempt trasmissio. This happes oly whe the bridge s packet buffer is empty. I order to fid this probability, we must deploy queuig theory ad we have to kow the arrival process to the bridge s queue, the size of the bridge s queue, ad the probability distributio packet service time by which packets depart from the queue. Therefore, Markov chai model ad queuig model of the bridge are coupled ad have to be modeled ad solved simultaeously. We will first solve the Markov chai for CSMA-CA MAC usig the variable π 11, which represets the probability that bridge s buffer is empty after the packet departure. Sice similar Markov chai models have bee solved with detailed steps of settig trasitio probabilities i the past i [9 12], we will just state the most importat steps i derivatio of access probability. Markov chai {st), bt)} is discrete as trasitios are observed at eds of slot times. It is bidimesioal give that γ 11 ad p b are idepedet of backoff stage) where st) represetsbackoff stage ad bt) represets value of backoff couter. Correspodig states of the Markov chai will have the state probabilities y i,j, i =,..., m 11, j =,..., W 11,i 1. Sice packet sizes i this applicatio are relatively small, we have icluded the states whe trasmissio of RTS/CTS ad data packets is goig o. Access probability is equal to τ 11 = m 11 i= y i,. Probability of idle state whe bridge s buffer is empty is equal to P idle = τ 11γ 11 π 11,, 8) φ 11 where φ 11 deotes average packet arrival rate of the arrival process to the bridge ote that packet arrival process is ot Poisso whe packets arrive from IEEE BAN to the bridge). 7) By isertig all ecessary trasitio probabilities, we obtai m γ11 π 11, 11 ) j τ 11 = + γ 11 1 γ11 φ 11 j= j= m 11 W11,j 1 ) ) j γ 11 1 γ ) pbc Ct + p bs St ) 1 p b + W11,m11 1 ) ) m11+1) 1 γ 11 2 ) pbc Ct + p bs St ) 1 p b +γ 11 St + 1 γ 11 ) Ct ) Derivatio of Probability Distributio of Occupacy of Bridge s Buffer. As we metioed, we will assume that bridge s buffer has a ifiite capacity. Ratioale behid that is that bridge device ideed ca have much larger memory tha sesig device ad that utilizatio of the bridge is expected to be light-to-moderate. Therefore, bridge is ot expected to work i the regime close to its stability limit where it ca reject packets due to fiite buffer. I GTS-based bridge period betwee arrivals of IEEE superframes to the bridge is costat, ad bridge ca be modeled as D/G/1 queuig system modeled at Markov poits of packet departures from the bridge. Let us deote period of arrival of sesig iformatio from all the sesors to bridge as Φ 11 = 1/φ 11. As metioed earlier, if the umber of sesors 15 < 16, the Φ 11 = BI, ad if 15k 1) < 15 15k, the Φ 15 = kbi. Assume that PGF for the bridge s packet service time ca be expressed as the series as T 11 z) = k= t 11,k z k.probabilityofl, l =, 1,... arrivals of GTS superframes durig packet service time of the bridge has the value a 11,l = Prob [ l+1)φ ] 11 1 lφ 11 T 11 < l +1)Φ 11 = t 11,j. j=lφ 11 9) 1) PGF for the probability distributio of the umber of superframe arrivals durig packet service time by the 82.11b iterface is A 11 z) = l= a 11,l z l.aequatio which shows umber of packets i bridge s buffer left after the departure of the packet has the form l+1 π 11,l = π 11, a 11,l + π 11,j a 11,l j+1. 11) By multiplyig both left-had ad right-had side of 11) with z l ad summig over l =,...,, weobtaipgffor the umber of packets left i the bridge s queue after the departig packet Π 11 z) = l= π 11,l z l as Π 11 z) = A 11z) ) 1 ρ 11 1 z), 12) A 11 z) z where ρ 11 = φ 11 T 11 presets offered load to the bridge. j=1

8 8 Iteratioal Joural of Telemedicie ad Applicatios Access probability Backoff freeze probability Number bridges a) Access probability b) Probability of freeze i backoff period Success probability Probability that buffer is empty after packet departure c) Probability of successful trasmissio d) Probability that buffer is empty after departure Figure 5: Access probability, probability that backoff cout will be froze, probability of successful trasmissio, ad probability that buffer is empty after departig packet. Aalytical results are show as lies ad simulatio results are show as poits. Table 2: Tradeoff betwee packetizatio delay ad umber of samples carried i each superframe. BO value Period betwee Number of EKG samples beacos i the superframe 6.983s s s s 24 Table 3: Parameters used i the aalytical modelig. 2 2 SO ) BO ) 3 Raw data rate ) 25 Kbps Superframe size ) 48 bytes MAC ad payload data rate for 82.11b 2 Mbps Payload size of 82.11b packet 1 slots at 2 Mbps IEEE physical + MAC header size 16.4 slots 5.3. Output Process ad Throughput. Output process from bridge has the PGF for packet iterdeparture times as Δ 11 z) = 1 π 11, ) T11 z)+π 11, z Φ11 T 11 z). 13) Assumig that there are 11 bridges commuicatig with access poit throughput i 82.11b LAN ca be the preseted with expressio Θ 11 = 11 l 11 2 Δ 11, 14) where 2 slots correspod to header iformatio Distributio of Packet Waitig Time i Bridge s Buffer. Assumig FIFO service disciplie, packet arrivig at the bridge has to wait for the curretly trasmitted packet to depart ad for complete service time of all packets already queued. Accordig to reewal theory, remaiig service time of the packet has PGF [18] T + 11z) = 1 T11 z) ) T 11 1 z). 15)

9 Iteratioal Joural of Telemedicie ad Applicatios Average umber of packets left after departig packet a) Mea umber of packets behid departig packet Average packet iterdeparture time b) Mea packet iterdeparture time Offered load Throughput c) Offered load for oe bridge d) Throughput Figure 6: Mea umber of packets left i the bridge s queue after departig packet, mea packet iterdeparture time, bridge offered load, ad throughput. Aalytical results are show as lies, ad simulatio results are show as poits. The, PGF for the waitig time of the packet has the form W 11 z) = π 11, + π 11,1 T + 11z)+π 11,2 T + 11z)T 11 z) + π 11,3 T 11z) + T 11 z) ) 2 = π 11, + T 11z) + π 11,1 + π 11,2 T 11 z)+π 11,3 T11 z) ) 2 + ) = π 11, + T 11z) + Π 11 T11 z) ) π 11, T 11 z) = π 11, 1+T 11z) + 1 A 11 T11 z) ) ) A 11 T11 z) ). T 11 z) 16) Average delay ca be obtaied by differetiatig 16)ad applyig L Hospital s rule: W 11 = φ 11T 2) 11 2 ), 17) 1 ρ 11 where T 2) 11 deotes secod momet of packet service time. This result matches Pollaczek-Khichi mea value formula [19]. The complete access time which icludes waitig time ad service time of the target packet is the equal to S 11 = W 11 + T Performace Evaluatio of GTS Bridge i Cotiuous EKG Telemetry I this sectio, we preset performace results for GTS bridge betwee IEEE ad IEEE 82.11b deployed i cotiuous EKG telemetry. I desig of GTS bridge for EKG telemetry, we assume that superframe will cotai oly three GTS parts. First oe is maagemet slot used for cotrol commuicatio betwee IEEE mote ad the bridge. Secod part is used to carry digitized EKG samples, ad the third part should cotai ackowledgmet from bridge to mote. Duratio of these parts depeds o the duratio of superframe ad time distace betwee the beacos. For example, if SO =, the superframe icludig the beaco frame cotais 16 slots with three backoff periods each. Duratio of beaco frame is 3 bytes 3 backoff periods) sice beaco ca carry ackowledgmet iformatio for previous superframe. Miimal duratio of maagemet slot is three backoff periods 3 bytes). However, 14 slots are the left to carry samples ad packet autheticatio code.

10 1 Iteratioal Joural of Telemedicie ad Applicatios Average value of packet service time Stadard deviatio of packet service time Skewess of packet service time a) Mea packet service time b) Stadard deviatio of packet service time c) Coefficietofskewessofpacketservicetime Figure 7: Momets of packet service time. Aalytical results are show as lies ad simulatio results are show as poits Average value of access time Stadard deviatio of access time Skewess of access time a) Mea system time b) Stadard deviatio of system time c) Coefficietofskewessofsystemtime Figure 8: Momets of system access) time. Aalytical results are show as lies, ad simulatio results are show as poits. We assume that HMAC fuctio adopted is costructed from secure hash algorithm SHA-1 hash [6, 2]) which is a widely used cryptographic hash fuctio with a message digest output of 16 bits. Therefore, 4 bytes are left i the superframe which covers at least 2 digitized samples, that is, measuremet period of 1 secod. This cofirms that SO = is a correct choice as log as the superframes are set with the period less tha a secod. Choice of the BO parameter, that is, the period betwee the beacos is result of cotradictig requiremets Table 2 outlies our desig optios). First requiremet is related to low power cosumptio ad asks that BO is chose to be as large as possible, but still able to carry all the samples geerated durig beaco iterval preferably close to 1 secod). Secod requiremet is related to the packetizatio delay ad reliability. Low packetizatio delay requires small amout of data i the packet. Secod, both IEEE ad IEEE 82.11b ad eve IEEE Bluetooth if it happes to operate i viciity) operate i ISM bad ad cause iterferece to each other. Iterferece ca corrupt the whole superframe, ad, therefore, shorter superframe sizes are preferable. We cosider a ideal wireless chael without oise ad fadig). MAC ad physical layer parameters are give i Table 3 resultig i a period betwee the superframes of.123 secods. We have umerically solved the overall system of equatios uder varyig umber of bridge devices. Aalytical processig was doe usig Maple 11 from Maplesoft. We have also implemeted the simulatio model usig Petri Net simulatio egie Artifex [21]. Figures 5 ad 6 show values of basic etwork parameters whe the umber of bridges is varyig betwee 1 ad 19. Delays are show i umbers of IEEE 82.11b slots 2 microsecods). Although total etwork load is light, we observe that a icrease of the umber of devices uder costat load per device causes liear icrease of access probability, freeze probability, ad throughput; while at the same time, trasmissio success probability, probability that buffer is empty after departure experieces liear decrease. We also observe that aalytical show as lie) ad simulatio results show as poits) are close. Figures 7 ad 8 show first three momets of the packet service time ad packet access time which icludes waitig time i the queue ad packet service time. We observe that for a icrease of the average packet service time of 3%, stadard deviatio has icreased three times. We preset coefficiet of skewess which is derived as the ratio of the third momet of the probability distributio ad third power of stadard deviatio [22] which idicates symmetry of the probability distributio aroud the mea value. This coefficiet is close to zero for distributios

11 Iteratioal Joural of Telemedicie ad Applicatios a) Probability distributio of packet service time, 1 bridges b) Probability distributio of packet service time, 3 bridges c) Probability distributio of packet service time, 5 bridges d) Probability distributio of packet service time, 7 bridges g) Probability distributio of packet service time, 13 bridges e) Probability distributio of packet service time, 9 bridges h) Probability distributio of packet service time, 15 bridges j) Probability distributio of packet service time, 19 bridges f) Probability distributio of packet service time, 11 bridges i) Probability distributio of packet service time, 17 bridges Figure 9: Probability distributio of packet service time. which are symmetric aroud their mea values. However, calculated values of skewess parameter idicate high level of asymmetry, ad we have bee motivated to calculate complete probability distributios ad discuss them. Figures 9 ad 1 show probability distributios of packet service time ad packet waitig time obtaied aalytically for cases whe the umber of bridges icreases from 1 to 19 i steps of 2. For packet service time, each peak o the graph correspods to oe backoff attempt. We otice that for small umber of bridges, almost all packets are served i first backoff attempt. The begiig of the first peak is determied by the time to complete sigle packet

12 12 Iteratioal Joural of Telemedicie ad Applicatios e 5 6e 5 4e 5 2e 5 a) Probability distributio of packet waitig time, 1 bridges e 5 6e 5 4e 5 2e 5 b) Probability distributio of packet waitig time, 3 bridges e 5 6e 5 4e 5 2e 5 c) Probability distributio of packet waitig time, 5 bridges e 5 6e 5 4e 5 2e 5 d) Probability distributio of packet waitig time, 7 bridges e 5 6e 5 4e 5 2e 5 e) Probability distributio of packet waitig time, 9 bridges e 5 6e 5 4e 5 2e 5 f) Probability distributio of packet waitig time, 11 bridges e 5 6e 5 4e 5 2e 5 g) Probability distributio of packet waitig time, 13 bridges e 5 6e 5 4e 5 2e 5 h) Probability distributio of packet waitig time, 15 bridges e 5 6e 5 4e 5 2e 5 i) Probability distributio of packet waitig time, 17 bridges e 5 6e 5 4e 5 2e 5 j) Probability distributio of packet waitig time, 19 bridges Figure 1: Probability distributio of packet waitig time i bridges buffer. trasmissio without the backoff cout St = 69 slots. The width of the first peak correspods to the size of iitial backoff widow elarged by freezig. After first backoff, trasmissio is either successful or collided where collisio lasts for Ct = 29 slots which correspods to the distace betwee the peaks). As the umber of bridges icreases, the umber ad itesity of higher-order backoff attempts icreases ad higher-order peaks become more proouced. Situatio is similar with packet waitig time i the sese that its distributio becomes wider as the umber of bridges icreases. The first peak of this distributio comes from the residual packet service time of the packet curretly beig

13 Iteratioal Joural of Telemedicie ad Applicatios 13 trasmitted) without the collisio, ad it further wides with icreasig umber of backoff phases. Flat parts after the first oe are due to packet retrasmissios after collisio. Both distributios show that packet delay i ward etwork is radom with large variace as the umber of bridges icreases. This is bad ews for real-time payload trasmitted i the IEEE packets sice EKG samples have to be displayed i costat time periods. The results show are useful to determie the amout of playback bufferig for EKG data i order to esure itelligible display of data. 7. Coclusio I this paper, we have preseted the desig issues ad performace evaluatio of the bridge betwee the BAN implemeted usig beaco-eabled IEEE etwork ad IEEE 82.11b wireless LAN. Bridge has bee implemeted usig GTS feature of IEEE Performace results show that for small offered load ad very small packet sizes which carry EKG data with basic badwidth of 24 bps), large umber of devices geerates very wide probability distributio of the packet access time. Give that EKG data has to be displayed i real time, accurate estimatio of access delay is ecessary i order to dimesio bufferig at the receiver. We have show that probability distributios of packet service time ad packet waitig time caot be characterized usig first two momets, istead the whole probability distributios are eeded i order to accurately estimate bufferig delays at the receiver. Ackowledgmet This research is supported by the NSERC Strategic grat. Refereces [8] G. Aastasi, E. Borgia, M. Coti, ad E. Gregori, IEEE 82.11b ad hoc etworks: performace measuremets, Cluster Computig, vol. 8, o. 2-3, pp , 25. [9] G. Biachi, Performace aalysis of the IEEE distributed coordiatio fuctio, IEEE Joural o Selected Areas i Commuicatios, vol. 18, o. 3, pp , 2. [1] E. Ziouva ad T. Atoakopoulos, CSMA/CA performace uder high traffic coditios: throughput ad delay aalysis, Computer Commuicatios, vol. 25, o. 3, pp , 22. [11] Y. Xiao ad J. Rosdahl, Throughput ad delay limits of IEEE 82.11, IEEE Commuicatios Letters, vol. 6, o. 8, pp , 22. [12] H. Zhai, Y. Kwo, ad Y. Fag, Performace aalysis of IEEE MAC protocols i wireless LANs, Wireless Commuicatios ad Mobile Computig, vol. 4, o. 8, pp , 24. [13] H. Zhai, X. Che, ad Y. Fag, How well ca the IEEE wireless LAN support quality of service? IEEE Trasactios o Wireless Commuicatios, vol. 4, o. 6, pp , 25. [14] J. Hui ad M. Devetsikiotis, A uified model for the performace aalysis of IEEE 82.11e EDCA, IEEE Trasactios o Commuicatios, vol. 53, o. 9, pp , 25. [15] X. Che, H. Zhai, X. Tia, ad Y. Fag, Supportig QoS i IEEE 82.11e wireless LANs, IEEE Trasactios o Wireless Commuicatios, vol. 5, o. 8, pp , 26. [16] Y. Xiao, Performace aalysis of priority schemes for IEEE ad IEEE 82.11e wireless LANs, IEEE Trasactios o Wireless Commuicatios, vol. 4, o. 4, pp , 25. [17] J. Mišić ad V. B. Mišić, Wireles Persoal Area Networks: Performace Itercoectios ad Security with IEEE , Joh Wiley & Sos, New York, NY, USA, 28. [18] H. Takagi, Queueig Aalysis. Volume 1: Vacatio ad Priority Systems, North-Hollad, Amsterdam, The Netherlads, [19] L. J. Kleirock, Queueig Systems. Volume 1: Theory, Joh Wiley & Sos, New York, NY, USA, [2] B. Scheier, Applied Cryptography, Joh Wiley & Sos, New York, NY, USA, 2d editio, [21] RSoft Desig, Artifex v.4.4.2, RSoft Desig Group, Ic., Sa Jose, Calif, USA, 23. [22] P. Z. Pebbles Jr., Probability, Radom Variables, ad Radom Sigal Priciples, McGraw-Hill, New York, NY, USA, [1] V. Shayder, B. Che, K. Loricz, T. R. F. Fulford-Joes, ad M. Welsh, Sesor etworks for medical care, Tech. Rep. TR- 8-5, Harvard Uiversity, Cambridge, Mass, USA, 25. [2] T.R.F.Fulford-Joes,G.-Y.Wei,adM.Welsh, Aportable, low-power, wireless two-lead EKG system, i Proceedigs of the 26th Aual Iteratioal Coferece of the IEEE Egieerig i Medicie ad Biology EMBC 4), vol. 3, pp , Sa Fracisco, Calif, USA, September 24. [3] E. Hartma, ECG frot-ed desig is simplified with microcoverter, Aalog Dialogue, vol. 37, o. 4, pp. 1 5, 23. [4] P. O. Bobbie, H. Chaudhari, C. Z. Arif, ad S. Pujari, Electrocardiogram EKG) data acquisitio ad wireless trasmissio, WSEAS Trasactios o Systems, vol. 3, o. 8, pp , 24. [5] M. Bishop, Computer Security: Art ad Sciece, Pearso Educatio, Bosto, Mass, USA, 23. [6] W. Stalligs, Cryptography ad Network Security: Priciples ad Practice, Pretice Hall, Upper Saddle River, NJ, USA, 3rd editio, 23. [7] Stadard for part 15.4: wireless MAC ad PHY specificatios for low rate WPAN, IEEE Std , IEEE, New York, NY, USA, October 23.