wireless sensor networks in healthcare applications 
 require small lightweight devices with sensing , computational , and communication 
 features to be unobtrusively placed on patient 's body . they need to communicate 
 results of sensing of healthcare data periodically over very short range to the 
 devices which can be carried by the patient or mounted on patient 's bed . we 
 refer to the wireless sensor network on patient 's body as body area network 
 ( ban ) . low power , that is , short communication range of wireless sensors is 
 needed for health , interference , and security reasons . devices which collect 
 the results of measurements need to provide some limited data processing and 
 aggregation , add security / privacy functions , and communicate aggregated data to 
 the lan access point in patient 's ward room as shown in figure 1 . , we consider interconnection of ieee 
 802.15.4 beacon - enabled network cluster with ieee 802.11b network . the ieee 
 802.15.4 nodes comprise patient 's body area network ( ban ) and are involved in 
 sensing some health - related data which will be transmitted to the access point 
 in the ward room using wireless technology such as ieee 802.11b . it is clear 
 that the network performance depends on the characteristics of the interconnection 
 device . therefore , we model the interconnected network where ieee 
 802.15.4-based ban operates in guaranteed time slot ( gts ) mode , and ieee 
 802.11b part of the bridge conveys gts superframe to the 802.11b access point . we then analyze the impact of important parameters such as acceptable load 
 ranges and the delays of communication due the increasing number of patients . since real - time operation of the bridges is necessary for many measurements in 
 hospitals besides intensive care units ( icus ) , we will study communications 
 through the bridge for simple case of ekg continuous telemetry . we 
 review the networking aspect of healthcare wireless sensor networks with the 
 emphasis on continuous electrocardiogram telemetry in section 2 . in section 3 , 
 we review the properties of 802.15.4 beacon - enabled mac and ieee 802.11b mac 
 related to the operation of bridge . in section 4 , we present the concepts of 
 bridge design between ieee 802.15.4 ban and ieee 802.11b ward lan . analytical 
 model of bridge where ban operates in gts mode is presented in section 5 . in 
 section 6 , in today 's hospitals , there is an urgent need for 
 timely monitoring the health status of many patients , especially those with 
 respiratory and cardiac problems . the need for continuous fetal heart rate 
 monitoring as well as monitoring for movements of patients suffered from stroke 
 or parkinson 's disease is also high . although these applications require 
 different kinds of sensors to measure levels of oxygen in blood , heart rate , or 
 motion of body parts , there is unified need for sensors to be unobtrusively 
 attached to the patient 's body and for measured data to be transmitted in a 
 reliable and secure way in order to be recorded on monitoring devices in real 
 time . most of the health variables are periodic and have to be periodically sampled 
 and digitized . the sampling period has to be at least twice as large as the 
 highest frequency of the healthcare variables . recently , several medical telemetry applications have 
 been prototyped so far and moved to production phase such as pulse oximeters , 
 ekg devices , and motion analysis systems . wireless transmission is currently implemented using 
 bluetooth ieee 802.15.1 and ieee 802.11b technologies although ieee 802.15.4 
 emerges as most suitable for medical applications due to its low - power and 
 low - bandwidth requirements . however , current reports on wireless healthcare 
 products are focused on reliable hardware and software designs of sensor 
 modules while the wireless transmission has been considered in testing phase 
 and for single device only . there is an area of research involving coordination 
 and real - time transmission of large number of healthcare measurements , which 
 has not attracted sufficient attention . in this paper interconnection of low - power ieee 802.15.4 motes 
 ( which are convenient for attachment on patient 's body ) with ieee 802.11b 
 network which has larger bandwidth and larger transmission range . we will 
 design bridge between ieee 802.15.4 wireless communication interface(s ) 
 residing at patient 's body and ieee 802.11b residing at bedside or carried in 
 patient 's pocket . more specifically , we will use tdma feature of ieee 802.15.4 
 called guaranteed time slots to fill it with digitized samples and pass it to 
 the interface of ieee 802.11b for further transmission to the hospital room 's 
 access point.analysis of delay of real - time health measurement 
 data incurred by transmission technologies . we will use measurement data for 
 electrocardiogram and analyze traffic when the number of patients increases . interconnection of low - power ieee 802.15.4 motes 
 ( which are convenient for attachment on patient 's body ) with ieee 802.11b 
 network which has larger bandwidth and larger transmission range . we will 
 design bridge between ieee 802.15.4 wireless communication interface(s ) 
 residing at patient 's body and ieee 802.11b residing at bedside or carried in 
 patient 's pocket . more specifically , we will use tdma feature of ieee 802.15.4 
 called guaranteed time slots to fill it with digitized samples and pass it to 
 the interface of ieee 802.11b for further transmission to the hospital room 's 
 access point . analysis of delay of real - time health measurement 
 data incurred by transmission technologies . we will use measurement data for 
 electrocardiogram and analyze traffic when the number of patients increases . , we will also address data integrity 
 issue by assuming that there is a shared secret key between 802.15.4 sensor 
 mote and bridge device . secret key will be used to provide message 
 authentication code in each 802.15.4 superframe ( packet ) using hmac function 
 [ 5 , 6 ] . electrocardiogram ( ecg or ekg ) is a surface 
 measurement of the electrical potential generated by the electrical activity , 
 which controls pumping action of cardiac muscle fibers . these electrical 
 impulses generate voltage , which further generates current flow in the torso 
 and potential differences on the skin . standard ekg monitoring involves 
 short - term ( 30 seconds ) monitoring of heart pulses using 
 12 skin electrodes ( called leads ) placed at designated locations on the 
 patient 's body including chest , arms , and legs . each pair of leads measures 
 voltage which gives one aspect of the heart 's activity . an ekg picture produced 
 by 12 leads allows diagnosis of wide range of heart problems . however , this 
 measurement is short - term and requires wired connection between the patient and 
 electrocardiograph . in many cases , however , it is necessary to have 
 continuous and tetherless measurements of heart rate . for such application , 
 only three leads placed at patient 's upper and lower chest can trace a wide 
 range of cardiac arrhythmias . one node of these three collects signals , 
 amplifies the signal difference , samples the amplified analog signal , and 
 digitizes it . standard clinical ekg application has the bandwidth of 0.05 hz to 
 100 hz . for pacemaker detection , upper frequency can be up to 1 khz there are 
 many design issues out of scope of this work related to noise suppression and 
 filtering frequencies from power line and respiration . in this paper , we assume 
 that upper frequency of the ekg signal is 100 hz . ekg signal is sampled with 
 200 hz , and each sample is digitized with 12 bits . therefore , basic bandwidth of ekg signal in standard 
 continuous telemetry is only 2400 bps . in beacon - enabled networks , the personal area network 
 ( pan ) coordinator divides its channel time into superframes . each superframe begins with 
 the transmission of a network beacon , followed by an active portion and an 
 optional inactive portion , as shown in figure 2 . the coordinator interacts with 
 its pan during the active portion of the superframe , and may enter a low - power 
 mode during the inactive portion . raw data rate in industrial , scientific , and 
 medical ( ism ) band is 250 kbps . duration of active and inactive parts of the 
 superframe is regulated with mac parameters so = 0 ,  , 14 which is known as macsuperframeorder and bo = 0 ,  , 14 , also called macbeaconorder . each slot consists of 32 backoff periods , which gives the shortest 
 active superframe duration abasesuperframeduration of 48 backoff periods 
 when so = 0 . duration of an active superframe part is denoted as sd = abasesuperframeduration   2 ( superframe duration ) . the time interval 
 between successive beacons is equal to bi = abasesuperframeduration  2 . the duration of the inactive period of the superframe can be determined as i = abasesuperframeduration  ( 2  2 ) . period between the beacons is equal to the active superframe duration only if 
 there is no inactive period in the cluster time , and , otherwise , it is larger 
 than active superframe part , that is , bo  so . an active superframe part consists of contention part 
 and tdma , that is , guaranteed time slot ( gts ) part . data transfer from a node to 
 pan coordinator can be done in gts slots or using slotted csma - ca access 
 described below . slotted csma - ca algorithm consists of backoff activity , two 
 clear channel assessments ( ccas ) , packet transmission , and optionally receipt 
 of the acknowledgment . backoff value is uniformly chosen in the range ( 0 , w15  1 ) which is called contention window . during 
 backoff countdown node does not listen to the medium , and checks the activity 
 on the medium only twice when backoff count is finished . by default , the node 
 can have m15 + 1 = 5 transmission attempts with backoff window 
 sizes w15,0 = 8 , w15,1 = 16 , w15,2 = 32 , w15,3 = 32 , and w15,4 = 32 . to avoid confusion , we will use subscript 15 to label mac parameters which have 
 their counterparts in the ieee 802.11b standard . ieee 802.11 has much more sophisticated csma - ca scheme 
 at the mac layer . in this protocol ( opposite to ieee 802.15.4 ) , a station 
 having a packet to transmit must initially listen to the channel to check if 
 another station is transmitting . if there is no transmission in distributed 
 interframe space ( difs ) time interval , the transmission can proceed . if medium 
 is busy , the station has to wait until current transmission has finished . then , 
 station will wait for difs time period and then generate a random backoff time 
 before transmitting its frame . this backoff time is uniformly chosen in the 
 range ( 0 , w11  1 ) . backoff counter will be decremented after 
 each slot time given that 
 transmission medium is free , otherwise , its value will be frozen until medium 
 becomes free again for difs time units ( slot time is derived from the 
 propagation delay time to switch from receiving to transmitting mode and time 
 to pass the information about the physical channel state to mac layer when the packet is 
 received , receiver replies with acknowledgment ( ack ) packet after short 
 interframe space ( sifs ) time interval . whenever packet collision occurs , 
 acknowledgment will not be received within sifs + ack time , and transmission 
 has to be reattempted with doubled contention window . if starting window size 
 is w11 = w11,min after m11 retransmissions , its maximal value will become w11,max = 2 w11,min ( in order to distinguish between similar 
 variables in two standards , we use subscript 11 ) . in our model , we assume that 
 if packet experiences more than m11 collisions , last backoff stage will be entered 
 for every subsequent retransmission until frame is successfully transmitted . in 
 order to limit packet collision time , and guard against hidden terminal 
 problem , the standard allows small reservation packets request to send ( rts ) 
 and clear to send ( cts ) sent using csma - ca . after transmission of rts packet , 
 receiver replies with cts after short interframe space(sifs ) time . due to 
 sensitivity of healthcare applications , we will assume that rts / cts scheme is 
 used to protect packets with measurement data of health variables . the ieee 802.11b standard is mostly deployed in 
 current implementations of healthcare wireless sensor networks . the ieee 802.11b has 
 higher - speed physical layer than original ieee 802.11 and allows transmissions 
 at 1 , 2 , 5.5 , and 11 mbps , while ieee 802.11 supports transmission at 2 mbps . however , physical layer header is transmitted at 1 mbps , mac layer header and 
 payload can be transmitted at 1 , 2 , 5.5 , or 11 mbps while control frames rts , 
 cts , and ack are transmitted at 1 or 2 mbps . it is also worth noting that since 
 ieee 802.11b adapters transmit at a constant power , distances covered with 
 transmission speeds of 1 , 2 , 5.5 , and 11 mbps are 120 , 90 , 70 , and 30 m , 
 respectively . starting with seminal work in , performance of ieee 802.11 
 has been extensively studied first for saturated case and later for unsaturated 
 case [ 1013 ] . standard extension ieee 
 802.11e enhances csma - ca access by introducing different interframe spaces and 
 different backoff window ranges for different traffic classes . this scheme has 
 been modeled using similar approach ( although more complex ) as basic 802.11 
 scheme in [ 1416 ] . however , given the fact 
 that all bans have the same priority and short packet sizes with sensing 
 information , we believe that ieee 802.11b can serve the purpose and that 
 deployment of ieee 802.11e at this point may not be necessary . these two components are interconnected 
 through a buffer which is filled by the pan coordinator and emptied by ieee 
 802.11b packet transmission facility . ieee 802.15.4 pan coordinator interface 
 and ieee 802.11b interface have their wireless transmit / receive antennas . both 
 networks operate in ism band as shown in figure 3 , and there is a need to 
 coordinate operation of bridge 's interfaces either in tdma or fdma manner . from 
 figure 2 and discussion in section 3.1 , we observe that it is possible to 
 achieve tdma coordination between the interfaces using the fact that wlan 
 bridge interface can operate during silent ban periods . however , in the presence 
 of multiple bans within wlan coverage , this approach requires synchronization 
 of ban beacons ( we assume that interference among bans is avoided by separation 
 in space or by allocating separate channels as shown in figure 3 ) . also 
 bandwidth allocation through so and bo parameters must be achieved such that bridged 
 traffic from all bans can be delivered during ( common ) inactive superframe 
 part . it is much more convenient if operation of ban and 
 wlan is separated in frequency domain because ban beacons do not need to be 
 synchronized and more bandwidth is allocated to the bridge . ban channels should 
 be chosen in such way that they do not overlap with ward wlan channel . from 
 figure 3 , we see that each wlan channel overlaps with four ban channels . 
 therefore , for each ward wlan channel , 12 out of 16 ban channels should be used 
 in order to avoid interference . duration of beacon interval bi is tuned according to period of sensed health 
 variable . duration of active period sd is chosen in order toachieve data transmission with high success 
 probability in the case of csma - ca mac , in case of gts transmission of sensed data , 
 gts bandwidth has to match necessary size of a group of gts packets and 
 acknowledgment lanes where group size corresponds to the number of ieee 
 802.15.4 nodes in ban . however , some small contention periods must be reserved 
 in the superframe in order to communicate command frames between sensing nodes 
 and pan coordinator . achieve data transmission with high success 
 probability in the case of csma - ca mac , in case of gts transmission of sensed data , 
 gts bandwidth has to match necessary size of a group of gts packets and 
 acknowledgment lanes where group size corresponds to the number of ieee 
 802.15.4 nodes in ban . however , some small contention periods must be reserved 
 in the superframe in order to communicate command frames between sensing nodes 
 and pan coordinator . since bandwidth of ieee 802.11b is much larger than 
 the bandwidth of ieee 802.15.4 ban , transmission of one ieee 802.11b packet will 
 take short time , and rest of active period can be used to exchange some command 
 data between the bridge and access point of the ward room . between two 
 transmission phases , sensing nodes and bridge are idle and can turnoff their 
 transmitters and receivers . we make an important remark about time scales in ieee 802.15.4 and ieee 
 802.11b . duration of backoff period in 802.15.4 is 320 microseconds , and with 
 raw data rate of 250 kbps , one backoff period carries 10 bytes of data . on the other hand , ieee 
 802.11b backoff counter is decremented after slot time which is equal to 20 
 microseconds . therefore , time - scale translation is needed between two networks . we assume that traffic intensity due to sensing of 
 health variables in ban will be light given that the number of nodes is lower 
 than 16 , and that offered load per node is lower than few kbps . bridge 's buffer will be served by ieee 802.11b csma - ca mac for which the markov chain model is presented in figure 4 . in our modeling , we will assume that data buffers at ban nodes and at the 
 bridge are infinite . although , this assumption may appear unrealistic for 
 sensor nodes ( and we have always modeled small finite buffers in our work 
 ) ; offered load to 
 the node is low so that node 's buffer is empty most of the time . therefore , 
 both the queuing model with finite and infinite buffers will give similar 
 results . given the lower computational complexity of the model with infinite 
 buffer , we use it in our analysis although use of finite buffer model is 
 straightforward . assumption of infinite buffer at the bridge is reasonable 
 since it may contain more complex hardware and software , and offered load per 
 bridge is low - to - moderate , depending on the number of patients in vicinity of 
 access point . in general case of gts , bridge sensors may report 
 different medical variables , such as heart rate , level of oxygen in blood , and 
 temperature . each sensor is allocated a number of slots in uplink direction to 
 carry uplink sensing data and a slot in downlink direction to carry 
 acknowledgment . we will refer to the number of slots in uplink direction 
 as packet lane . pan coordinator receives data from stations in 
 separate gts packet lanes , generates acknowledgments , and passes aggregated 
 packets to ieee 802.11b buffer . this results in allocation of ds packet lanes such that 
 ( 1)ds  =  ds32so80482bo0.00032 , 
 and that period between the 
 beacons bi = 48  2  0.00032 matches the sampling period of health 
 variable . assuming that there are n15 < 16 sensors in the ban , each sensor will have one 
 gts slot , and the last slot will contain aggregated acknowledgments for all 
 sensors . for larger number of sensors where 15(k  1 ) < n15  15k period between the beacons has to be decreased k times , such that each superframe carries 
 readings from at most 15 sensors ( and acknowledgments in the last gts slot ) . for simplicity , let n15 < 16 and the payload of the ieee 802.15.4 
 superframe becomes payload of ieee 802.11b frame consisting of n15ds3210 bytes . ieee 802.11b frame length in bytes has to be augmented with headers from physical and mac 802.11b layer which is 50 
 bytes . finally , we have to find frame size in 802.11b slots ( backoff periods ) , 
 since each slot carries number of bits s11 equal to the product of raw data rate and slot 
 duration , and its value is equal to l11 = ( 50 + n15ds3210)/s11 . duration of rts , cts , and ack frames expressed in 
 slots will be denoted as rts , cts , and ack11 , respectively ( we will use subscript 11 to denote ieee 802.11b whenever 
 potential ambiguity may arise between two standards ) . duration of difs and sifs 
 periods in slots will be denoted as difs and sifs . probability generating function ( pgf ) for the 
 successful packet transmission time is equal to 
 ( 2)st(z )  =  zrts+cts+l11 + 3sifs+difs+ack11 , 
 with average value st  =  st(1 )  =  rts  +  cts  +  l11  +  3sifs  +  difs  +  ack11 . in the case of collision of rts packets activity on medium has pgf : 
 ( 3)ct(z )  =  zrts+cts+sifs+difs , 
 with average value ct  =  ct(1 )  =  rts  +  cts  +  sifs  +  difs . each bridge communicates the same kind of sensing traffic towards the 
 access point . using the assumption from previous work [ 25 , 9 , 14 , 15 ] that probability of 
 successful transmission is independent of the backoff stage relationship between these two probabilities is 
 ( 4)11  =  ( 111)(n111 ) . probability that medium will be active during the 
 backoff countdown of one station has two components . first one is the 
 probability that station sensed the medium busy due to successful transmission 
 of one among n11  1 stations , and it has the value pbs = ( n11  1)11(1  11 ) . the other component is the probability that station senses the medium busy due 
 to collision among some of n11  2 other stations and has the value pbc = 1  ( 1  11 )  pbs . their sum is the probability that medium is busy during the backoff countdown , 
 and that backoff counter is frozen pb = pbs + pbc = 1  11 . the pgf for the duration of time between two successive backoff countdowns is 
 represented with the following equation : 
 ( 5)hd(z )  =  z11+(pbcct(z )  +  pbsst(z))hd(z ) . 
  at this point , we note that duration of period between 
 two successive decrements of backoff counter is limited to the maximum packet 
 size . after transmission is finished and difs period passes any station doing 
 the backoff , countdown has to decrement its backoff counter at least once 
 before packet transmission : 
 ( 6)b11,i(z )  =  k=0w11,i11w11,ihdk(z )  =  hdw11,i(z)1w11,i(hd(z)1 ) , 
 where w11,i = 2 
				 w11,0 for i  m11 , and w11,i = 2 
				 w11,0 for i > m11 . assuming that packet will be retransmitted until valid 
 acknowledgement is received , the pgf for the packet service time 
 becomes 
 ( 7)t11(z )  =  i=1m11 + 1(j=0i1b11,j(z))(111)(i1)ct(z)(i1)11st(z ) +  ( j=0m11b11,j(z))i = m11 + 1(b11,m11(z))(im11 )    ( 111)(i1)ct(z)(i1)11st(z ) , 
 and its average value is obtained as t11  =  t11(1 ) . in the derivations above , we have derived probability 
 of successful transmission and probability of freezing the backoff period using 
 the variable which represented access probability per 802.11b slot 11 . access probability , on the other hand , has to be derived using two modeling 
 components . first one is the markov chain which represents conditional 
 activities within the csma - ca process . second component indicates the 
 probability that bridge will be idle and that it will not perform backoff count 
 and attempt transmission . this happens only when the bridge 's packet buffer is 
 empty . in order to find this probability , we must deploy queuing theory and we 
 have to know the arrival process to the bridge 's queue , the size of the 
 bridge 's queue , and the probability distribution packet service time by which 
 packets depart from the queue . therefore , markov chain model and queuing model 
 of the bridge are coupled and have to be modeled and solved simultaneously . we 
 will first solve the markov chain for csma - ca mac using the variable 11,0 which represents the probability that bridge 's 
 buffer is empty after the packet departure . since similar markov chain models have been solved 
 with detailed steps of setting transition probabilities in the past in 
 [ 912 ] , we will just state the 
 most important steps in derivation of access probability . markov chain { s(t ) , b(t ) } is discrete as transitions are observed at ends of slot times . it is bidimensional ( given that 11 and pb are independent of backoff stage ) where s(t ) represents backoff stage and b(t ) represents value of backoff counter . corresponding states of the markov chain will have the state probabilities yi , j , i = 0 ,  , m11 , j = 0 ,  , w11,i  1 since packet sizes in this application are relatively small , 
 we have included the states when transmission of rts / cts and data packets is going on . probability of idle state when bridge 's buffer is 
 empty is equal to 
 ( 8)pidle  =  111111,011 , 
 where 11 denotes average packet arrival rate of the 
 arrival process to the bridge ( note that packet arrival process is not poisson 
 when packets arrive from ieee 802.15.4 ban to the bridge ) . by inserting all necessary transition probabilities , 
 we obtain 
  ( 9)11  =  ( 1111,011+j=0m1111(111)j+  j=0m11(w11,j1)11(111)j2(1pb)(pbcct+pbsst )  +  ( w11,m111)(111)(m11 + 1)2(1pb)(pbcct+pbsst)+11st+(111)ct)1 . as we mentioned , we will assume that bridge 's buffer 
 has an infinite capacity . rationale behind that is that bridge device indeed 
 can have much larger memory than sensing device and that utilization of the 
 bridge is expected to be light - to - moderate . therefore , bridge is not expected 
 to work in the regime close to its stability limit where it can reject packets 
 due to finite buffer . in gts - based bridge period between arrivals of ieee 
 802.15.4 superframes to the bridge is constant , and bridge can be modeled as 
 d / g/1 queuing system modeled at markov points of packet departures from the 
 bridge . let us denote period of arrival of sensing information from all the 
 sensors to bridge as 11 = 1/11 . as mentioned earlier , if the number of sensors n15 < 16 ,   then 11 = bi , and if 15(k  1 ) < n15 15k , then 15 = kbi . assume that pgf for the bridge 's packet service time can be expressed as the 
 series as t11(z ) = k = 0 
 t11,k 
 z. probability of l , l = 0 , 1 ,    arrivals of gts superframes during packet 
 service time of the bridge has the value 
 ( 10)a11,l  =  prob[l11t11<(l+1)11]=j = l11(l+1)111t11,j . pgf for the probability distribution of the number of 
 802.15.4 superframe arrivals during packet service time by the 802.11b 
 interface is a11(z ) = l = 0 
 a11,l 
 z. an equation which shows number of packets in bridge 's buffer left after the 
 departure of the packet has the form 
 ( 11)11,l  =  11,0a11,l  + j=1l+111,ja11,lj+1 . 
 by multiplying both left - hand 
 and right - hand side of ( 11 ) with z and summing over l = 0 ,  , , we obtain pgf for the number of packets left in the bridge 's queue 
 after the departing packet 11(z ) = l = 0 
 11,l 
 z as 
 ( 12)11(z )  =  a11(z)(111)(1z)a11(z)z , 
 where 11  =  11t11 presents offered load to the bridge . output process 
 from bridge has the pgf for packet interdeparture times as 
 ( 13)11(z )  =  ( 111,0)t11(z )  +  11,0z11t11(z ) . assuming that there are n11 bridges communicating with access point 
 throughput in 802.11b lan can be then presented with expression 
 ( 14)11  =  n11l11211 , 
 where 2 slots correspond to header information . assuming fifo service discipline , packet arriving at the bridge has to wait for the currently 
 transmitted packet to depart and for complete service time of all packets 
 already queued . according to renewal theory , remaining service 
 time of the packet has pgf 
 ( 15)t11+(z )  =  ( 1t11(z))t11(1z ) . 
  then , pgf for the waiting time of the packet has the form 
 ( 16)w11(z)=  11,0  +  11,1t11+(z )  +  11,2t11+(z)t11(z )  +  11,3t11+(z)(t11(z))2=  11,0  +  t11+(z)(11,1  +  11,2t11(z )  +  11,3(t11(z))2+)=  11,0  +  t11+(z)11(t11(z ) )    11,0t11(z)=  11,0(1  +  t11+(z)1    a11(t11(z))a11(t11(z))t11(z ) ) . average delay can be obtained by differentiating ( 16 ) 
 and applying l'hospital 's rule : 
 ( 17)w11  =  11t11(2)2(111 ) , 
 where t11 denotes second moment of packet service time . the complete access time which includes waiting time 
 and service time of the target packet is then equal to s11  =  w11  +  t11. in this section , we present performance results for 
 gts bridge between ieee 802.15.4 and ieee 802.11b deployed in continuous ekg 
 telemetry . in design of gts bridge for ekg telemetry first one is management slot used for 
 control communication between ieee 802.15.4 mote and the bridge . second part is 
 used to carry digitized ekg samples , and the third part should contain 
 acknowledgment from bridge to mote . duration of these parts depends on the 
 duration of superframe and time distance between the beacons . for example , if so = 0 , 
 then superframe including the beacon frame contains 16 slots with three backoff 
 periods each . duration of beacon frame is 30 bytes ( 3 backoff periods ) since 
 beacon can carry acknowledgment information for previous superframe . minimal 
 duration of management slot is three backoff periods ( 30 bytes ) . however , 14 
 slots are then left to carry samples and packet authentication code . we assume 
 that hmac function adopted is constructed from secure hash algorithm ( sha-1 
 hash [ 6 , 20 ] ) which is a widely used 
 cryptographic hash function with a message digest output of 160 bits . therefore , 400 bytes are left in the superframe which covers at least 200 
 digitized samples , that is , measurement period of 1 second . this confirms that so = 0 is a correct 
 choice as long as the superframes are sent with the period less than a second . choice of the bo parameter , that is , the period between the 
 beacons is result of contradicting requirements ( table 2 outlines our design 
 options ) . first requirement is related to low power consumption and asks that bo is chosen to be as large as possible , but 
 still able to carry all the samples generated during beacon interval ( preferably 
 close to 1 second ) . second , both ieee 802.15.4 and ieee 802.11b ( and even ieee 802.15 1 
 bluetooth if it happens to operate in vicinity ) operate in ism band and cause 
 interference to each other . interference can corrupt the whole superframe , and , 
 therefore , shorter superframe sizes are preferable . mac and physical layer parameters are given in table 3 resulting 
 in a period between the superframes of 0.123 
 seconds . we have numerically solved the overall system of 
 equations under varying number of bridge devices . figures 5 and 6 show values of basic network 
 parameters when the number of bridges is varying between 10 and 190 . although total 
 network load is light , we observe that an increase of the number of devices 
 under constant load per device causes linear increase of access probability , 
 freeze probability , and throughput ; while at the same time , transmission 
 success probability , probability that buffer is empty after departure 
 experiences linear decrease . we also observe that analytical ( shown as line ) 
 and simulation results ( shown as points ) are close . figures 7 and 8 show first three moments of the packet 
 service time and packet access time which includes waiting time in the queue 
 and packet service time . we observe that for an increase of the average packet 
 service time of 30% , standard deviation has increased three times . we present 
 coefficient of skewness which is derived as the ratio of the third moment of 
 the probability distribution and third power of standard deviation   which indicates symmetry of 
 the probability distribution around the mean value . this coefficient is close 
 to zero for distributions which are symmetric around their mean values . however , calculated values of skewness parameter indicate high level of 
 asymmetry , and we have been motivated to calculate complete probability 
 distributions and discuss them . figures 9 and 10 show probability distributions of 
 packet service time and packet waiting time obtained analytically for cases 
 when the number of bridges increases from 10 to 190 in steps of 20 . for packet 
 service time , each peak on the graph corresponds to one backoff attempt . we 
 notice that for small number of bridges , almost all packets are served in first 
 backoff attempt . the beginning of the first peak is determined by the time to 
 complete single packet transmission without the backoff count st  =  69 slots . the width of the first peak corresponds 
 to the size of initial backoff window enlarged by freezing . after first 
 backoff , transmission is either successful or collided where collision lasts 
 for ct  =  29 slots ( which corresponds to the distance 
 between the peaks ) . as the number of bridges increases , the number and 
 intensity of higher - order backoff attempts increases and higher - order peaks 
 become more pronounced . situation is similar with packet waiting time in the 
 sense that its distribution becomes wider as the number of bridges increases . the first peak of this distribution comes from the residual packet service time 
 ( of the packet currently being transmitted ) without the collision , and it 
 further widens with increasing number of backoff phases . both distributions show that packet delay in ward 
 network is random with large variance as the number of bridges increases . this 
 is bad news for real - time payload transmitted in the ieee 802.11 packets since 
 ekg samples have to be displayed in constant time periods . the results shown 
 are useful to determine the amount of playback buffering for ekg data in order 
 to ensure intelligible display of data . in this paper , we have presented the design issues and 
 performance evaluation of the bridge between the ban implemented using 
 beacon - enabled ieee 802.15.4 network and ieee 802.11b wireless lan . performance results show 
 that for small offered load and very small packet sizes which carry ekg data 
 ( with basic bandwidth of 2400 bps ) , large number of devices generates very wide 
 probability distribution of the packet access time . given that ekg data has to 
 be displayed in real time , accurate estimation of access delay is necessary in 
 order to dimension buffering at the receiver . we have shown that probability 
 distributions of packet service time and packet waiting time can not be 
 characterized using first two moments , instead the whole probability 
 distributions are needed in order to accurately estimate buffering delays at 
 the receiver .
we consider interconnection of ieee 802.15.4 beacon - enabled network cluster with ieee 802.11b 
 network . 
 this scenario is important in healthcare applications where ieee 802.15.4 nodes comprise 
 patient 's body area network ( ban ) and are involved in sensing some health - related data . 
 ban nodes 
 have very short communication range in order to avoid harming patient 's health and save energy 
 . 
 sensed data needs to be transmitted to an access point in the ward room using wireless technology 
 with higher transmission range and rate such as ieee 802.11b . 
 we model the interconnected network 
 where ieee 802.15.4-based ban operates in guaranteed time slot ( gts ) mode , and ieee 802.11b 
 part of the bridge conveys gts superframe to the 802.11b access point . 
 we then analyze the 
 network delays . 
 performance analysis is performed using ekg traffic from continuous telemetry , and 
 we discuss the delays of communication due the increasing number of patients .