An Online Delay Efficient Multi-Class Packet Scheduler for Heterogeneous M2M Uplink Traffic

Transcription

1 An Onlne Delay Effcent Mult-Class Packet Scheduler for Heterogeneous M2M Uplnk Traffc Akshay Kumar, Ahmed Abdelhad and Charles Clancy Hume Center, Vrgna Tech Emal:{akshay2, aabdelhad, Abstract The sensory traffc n Machne-to-Machne (M2M) communcatons exhbt heterogenety n several dmensons such as packet arrval rate, delay tolerance requrements etc. However, the desgn of most of the exstng M2M packet schedulers do not account for ths ntrnsc heterogenety n sensor traffc. Therefore, motvated by ths, we study the delay-performance of a heterogeneous M2M uplnk channel from the sensors to the Programmable Logc Controller (PLC) n an ndustral automaton scenaro. Besdes the heterogenety across the sensors, the data from each sensor s also heterogeneous and can be classfed as ether Perodc Update (PU) or Event Drven (ED) data. The PU arrvals are perodc, synchronzed by the PLC and need to be processed by a prespecfed frm latency deadlne. On the other hand, the ED arrvals are random and have low-arrval rate wthout any hard servce deadlne. We map these contrastng arrval, servce characterstcs of PU and ED packets from dfferent sensor usng step and sgmodal functons of servce latency respectvely. Due to the heterogenety, the aggregated traffc at PLC forms multple queues/classes whch are then served so as to maxmze a proportonally-far system utlty. Specfcally the proposed mult-class scheduler gves prorty to ED data from dfferent sensors as long as the latency deadlne s met for the PU data. We mnmze successve PU falures usng novel penalty functons and clear faled PU packets to reduce network congeston. Usng extensve smulatons, we compare the performance of our scheme wth varous state-of-the art packet schedulers and show that t outperforms other schedulers when network congeston ncreases. The performance gap further ncreases wth heterogenety n latency requrements and ncrease n penalty for successve PU falures. Index Terms M2M, Latency, Qualty-of-Servce, MultClass Scheduler, Industral Automaton I. INTRODUCTION Automaton for ndustral montorng and control processes has become commonplace these days. It can be modeled as a star-topology Machne-to-Machne (M2M) network of varous process sensors communcatng wrelessly to a Programmable Logc Controller (PLC) on the uplnk channel whch then feeds back the output to a control devce ( downlnk channel ) to ensure the desred process operaton. Typcally, the ndustral M2M traffc has very low latency requrements (of order of few mllseconds). It can be broadly categorzed as ether non real-tme (no deadlne for task completon) or soft realtme (decreased utlty f deadlne not met) or frm (zero utlty f deadlne not met) or hard (system falure f deadlne not Ths research s based upon work supported by the Natonal Scence Foundaton under Grant No met). For nstance, the messages from a nstrumented protectve system or safeguardng system have hard real-tme servce requrements whereas preventve mantenance applcatons are typcally served n non real-tme. Wth ncrease n network sze, the avalable computatonal and communcaton resources gets shared among a large number of sensors. Ths makes t harder to provde real-tme servce due to smultaneous access attempts from multple sensors [] and also wastage of wreless spectrum contnuously allocated to sensors wth very low transmsson duty cycle [2]. Therefore n ths paper, we develop an onlne delay-effcent packet scheduler for heterogeneous M2M uplnk traffc. To begn wth, we use source M2M traffc model n [3] to classfy the sensor data nto Perodc Update (PU) and Event Drven (ED) packets. The PU arrvals are perodc wth frm latency deadlne whle the ED arrvals are random wthout hard servce deadlnes. Paper Contrbutons: We map the contrastng delay requrements of PU and ED packets from dfferent sensors usng step and sgmodal utlty functons. We defne the overall system utlty as the product of (tme) averaged utltes of all PU and ED traffc-classes n order to ensure proportonal farness. Our goal s to determne the optmal schedulng polcy that maxmzes the proposed system utlty. However, due to the randomness n arrval and servce tmes, there exsts no delayoptmal onlne algorthms [4]. Therefore, we propose an onlne delay-effcent mult-class heurstc scheduler for the uplnk traffc at the PLC, that gves prorty to ED data as long as that does not result n a utlty loss for the PU data. Ths results n a hgher utlty for the ED data. However as the sze of networks ncreases, PU packets ncreasngly fal to meet ther deadlnes. We remove the faled PU packets from the system to reduces congeston and thus mprove overall system utlty. Furthermore, snce successve packet drops are worse than solated packet drops, we ntroduce a novel penalty functon as part of PU utlty functon to reduce successve PU falures. Usng extensve smulatons, we show that ths results n an overall ncrease n system utlty as compared to other popular schedulng We assume frm servce deadlne for PU nstead of hard deadlne because typcally the perodc data does not change much from one perod to another, especally f the perod s small. So f a PU packet fals to meet servce deadlne, the PLC can use an estmate for the PU based on the recent hstory, albet wth some degradaton n utlty.

2 polces such as Frst-Come-Frst-Serve (), Earlest Due Date (), prorty schedulng etc. Lastly, the proposed scheduler s agnostc to the wreless technology beng used for the M2M uplnk and s also ndependent of the hardwaresoftware archtecture used n practcal real-tme embedded systems. Also t can easly adapt to accommodate tme-varyng arrval and servce rates for the PU and ED packets. Paper Outlne: The rest of the paper s organzed as follows. Secton II detals the related work. Secton III ntroduces the system model and defnes the utlty functons for PU and ED data. Then n Secton IV, we formulate the utlty maxmzaton problem and n Secton V descrbe the proposed schedulng scheme at PLC. Secton VI presents smulaton results. Fnally Secton VII draws some conclusons. II. RELATED WORK A number of pror works have looked nto ntegratng the desgn of real-tme schedulng schemes n mddle-ware based archtectures so as to meet the hard deadlne of real-tme servces. Tommaso et. al. n [5] presented a real-tme servce orented archtecture for ndustral automaton. However, these works are tangental to our lne of work n the sense that our proposed scheduler s agnostc of the hardware-mddlewaresoftware archtecture and maps the real-tme QoS requrements of M2M traffc nto utlty functons that needs to be maxmzed. Another lne of work focuses on QoS-aware packet scheduler for M2M traffc n Long Term Evoluton (LTE) network (see [6] and references theren). Most of these works use some varants of Access Grant Tme Interval scheme for allocatng fxed or dynamc access grants over perodc tme ntervals to M2M devces. Nusrat et. al. n [7] desgned a packet scheduler for M2M n LTE so as to maxmze the percentage of uplnk packets that satsfy ther ndvdual budget lmts. Unlke our work, these works desgn packet scheduler specfc to a wreless standard such as LTE and are thus heavly nfluenced by the Medum Access Control archtecture of LTE. Also unlke our work, they also don t focus on the heterogenety n packet rate, servce delay requrements of traffc from dfferent sensors. A number of schedulng algorthms have been proposed specfcally for real-tme embedded systems (see [8] and references theren) that are agnostc to the applcaton scenaro, wreless technology used or hardware-software archtecture. These schemes assume hybrd task sets comprsng of hard perodc requests and soft real-tme aperodc requests. The goal of all these schemes s to guarantee completon of servce (before deadlne) for all perodc request and smultaneously am to reduce the average response tmes of aperodc requests. They are broadly classfed nto Fxed-prorty and Dynamc prorty assgnments. Fxed prorty schemes schedule perodc tasks usng Rate-Monotonc algorthm but dffer n servce for aperodc tasks. Dynamc schedulng algorthms schedule perodc tasks usng scheme and allow better processor utlzaton and enhance aperodc responsveness as compared to the fxed prorty schemes. The drawbacks of these schemes Sensor 2 Sensor Sensor 3 Wreless PLC... Class - PU Class 2 - PU Class - ED Class 2 - ED λ pu λ 2 pu λ ed λ 2 ed Sensor N Fg.. System model llustratng queung process n the M2M uplnk. We consder only four dfferent classes for ease of llustraton. s that they assume that the servce tmes for each tasks are known apror. Hence they schemes are not truly onlne n ther present form and would requre consderable modfcatons. The work that s most closely related to our work s by Kumar et. al. n [9] wheren they proposed a delay-effcent heurstc packet scheduler for M2M uplnk. However ths work assumed the traffc orgnatng from dfferent sensors s dentcal havng same arrval rate, servce delay requrements etc. Also, unlke our work, ther proposed scheduler does not dfferentate between successve PU falures and solated PU falures. III. SYSTEM MODEL Fg shows the system model llustratng the queung process n the uplnk channel (.e., from sensors to the PLC) n an ndustral automaton settng. Each of the N sensors transmts two types of packets to the PLC: frequent perodc updates (PU) for some process related measurement or sporadc eventdrven (ED) packets trggered when the sensor measurement for a physcal quantty cross ts threshold. In the most general sense, the arrval rate and latency requrements of uplnk traffc s dfferent for each sensor. Therefore, we model the PU arrvals from the th sensor as a determnstc perodc process wth perod Tpu and thus rate λ pu = /Tpu whle the ED arrvals s modeled as a Posson process wth rate λ ed. Let s pu and s ed denote the sze for PU and ED packets from the th sensor. The servce tme for PU and ED packets from the th sensor are assumed to be exponental wth rate µ pu and µ ed respectvely, gven by µ pu = µ/s pu and µ ed = µ/s ed, () where µ s the servce rate at PLC per unt packet sze. In general, the total tme spent by a packet n the system, T, can

3 ) be wrtten as sum of followng components, T = T trans + T prop + T cong + T queue + T ser, (2) whch denote the followng component delays: T trans : Transmsson delay at the sensor. T prop : Propagaton delay from the sensor to PLC. T cong : Congeston delay due to shared wreless channel n large-scale sensor network. T queue : Queung delay at the PLC. T ser : Processng tme for a packet at the PLC. In ths work, we gnore all the terms except the queung delay at PLC T queue and the servce tme T ser. Ths s because the packet sze s usually qute small to gnore T trans and the sensors and PLC are usually close enough on the shop floor to permt the usage of low power wreless sgnalng and thus gnore T prop. Also, we assume that the avalable wreless spectrum s large enough to allocate a dedcated transmsson channel to each sensor; so there s no congeston delay T cong. In the most general case, the PU and ED packets from N sensors form 2N separate queues/traffc-classes. Now the queung delay for each class depends upon the schedulng polcy adopted at the PLC. The schedulng polcy at PLC should be chosen as to maxmally satsfy the latency constrants of PU and ED packets. IV. PROBLEM FORMULATION We frst map the latency requrements onto the utlty functons for the PU and ED classes as shown n Fg. IV-B and IV-B. A. Utlty Functons ) PU utlty: As stated prevously, the PU packets need to be processed wthn a prespecfed (usually by PLC) tme nterval at the end of whch there s no utlty n servng the packet. For a PU packet from th sensor wth latency lpu, we defne the utlty functon as, { Upu(l pu) f lpu < ld = f lpu ld, (3) where ld s the latency deadlne at whch utlty drops to. We now defne a penalty functon so as to lmt the number of consecutve PU packets that fal to meet the latency deadlne 2. Let r denote the run-length 3 of PU drops for th sensor, then the correspondng penalty s, P pu(r ) = r r γ, r (4) where γ s a penalty functon parameter denotng the degree of penalty for th sensor. γ = mples that we do not penalze consecutve PU drops. 2 Hereafter, we use the term PU drop to ndcate that PU packet fals to meet ts deadlne. 3 A run s a maxmal length sequence of consecutve dentcal outcomes wthn a larger sequence. For example, let [SSDDSDSDDDS] denote a sequence of PU success (S) and drops (D). Then we have three runs of PU drops of lengths, 2 and 3. (l pu Utlty of PU packet from th sensor, U pu Fg. 2. Latency of PU packet from th sensor, (l pu ) n ms l d = ms Utlty functon for PU packet. 2) ED utlty: Unlke, the PU packets, ED packets do not have a hard deadlne, rather ther utlty s a strctly decreasng functon of latency. We defne the ED utlty for th sensor as a sgmodal functon, as n [], [], gven by, ( ) Ued(l ed) = c + e d a(l ed b), (5) where, c = +ea b and d e a b = +e. We note that U a b ed () = and Ued ( ) =. The parameter a s the utlty roll-off factor whose value depends on the crtcalty of the applcaton. The nflecton pont of (5) occurs at led = b. B. System utlty functon For a gven schedulng polcy P, we frst defne a proportonally far system utlty functon as, V(P) = N U puβ pu (P) U edβ ed (P), (6) = where U pu(p) and U ed (P) are the average utlty of PU and ED packets n the steady state gven as, U pu(p) = lm T s U ed(p) = lm T s M pu (Ts) j= U pu(l,j pu (P)) R (T s) Med(T s) j= U ed (l,j M ed (T s ) j= Ppu(r,j (P)) Mpu(T, s ) (7) ed (P)), (8) where Mpu(T s ) and Med (T s) are the number of PU and ED packets from th sensor served n tme T s. R (T s ) denotes the number of runs of PU drops n tme T s and r,j denotes the run-length of j th PU drop for sensor. lpu,j and l,j ed denote the latency of the j th packet from th sensor of type PU and ED respectvely. The parameters βpu and βed denote the prorty gven to average PU and ED utlty for th sensor.

4 ) (l ed Utlty of ED packet from th sensor, U ed. a = ms - b = 2 ms Fg. 3. C. Optmal scheduler Latency of ED packet from th sensor (l ed ) n ms Utlty functon for ED packet. We now descrbe the utlty maxmzaton problem that needs to be solved to determne the optmal schedulng polcy at PLC. It s gven by, max P V(P) = N U puβ pu (P) U edβ ed (P). (9) = If the servce tmes of PU and ED were determnstc or known apror, then the optmal scheme s to schedule PU jobs from sensor, so that they are completed exactly at the deadlne ld. However, snce the arrval tme of ED packet, the servce tmes for PU and ED packets are random, t s not possble to determne an onlne optmal scheduler [4]. Therefore, we propose an onlne heurstc scheduler that ams to maxmze the utlty functon and s descrbed n the next secton. V. PROPOSED SCHEDULER A. Servce order between PU and ED classes The utlty of PU remans constant at untl the deadlne, at whch t drops to. Therefore, t would be best (from the perspectve of ED latency) to delay the servce of PU as much as possble but ensurng that we serve t before deadlne. However, the randomness n PU and ED servce tmes makes t hard to determne the optmal start of servce for each PU packet n real-tme. To overcome ths problem, our proposed scheduler gves prorty to ED packets as long as the current latency of PU packet from any sensor s less than ts preset threshold lt, ( < lt < ld ), =, 2,, N. If the latency of any PU packet exceed ts threshold whle PLC s processng any ED packet, then that ED packet gets mmedately preempted by the PU packet. Ths ensures that we reduce latency of ED packets whle ensurng that most of the PU packets meet ther latency deadlne. B. Servce order wthn PU classes We now dscuss how the proposed scheduler determnes the order of servce between packets of dfferent PU classes. It s more mportant to meet latency deadlne of PU class wth hgh arrval perod snce the sensor data may have changed substantally between two consecutve arrvals. Therefore, we prortze the servce of PU classes n decreasng order of arrval tme-perod,.e., PU class wth hghest arrval perod gets hghest (preemptve) prorty. However, smlar to prevous secton, the prorty of PU classes comes nto effect only when the packet latency exceeds ts correspondng latency threshold. C. Servce order wthn ED classes We now dscuss how the proposed scheduler determnes the order of servce between packets of dfferent ED classes. We assgn hgher prorty to ED classes that are more delay senstve (.e., have hgher a or lower b ). Unlke prevously, the prorty order among ED classes comes nto effect mmedately after the packet enters the system. However, f the latency of th ED class exceeds a certan threshold δ whle there are packet of lower prorty ED classes watng for servce, then ts gets preempted from server by the ED class wth next hghest prorty. By defnton, the threshold δ = for ED class wth least prorty. Ths preempton ensures that ED packets wth unusually large servce tme do not ncrease latency of subsequent packets. Thus, we reduce latency of delay-senstve ED class wthout ncurrng very large latency for delay-tolerant classes. Now, n order to maxmze the system utlty for gven set of system parameters, we need to determne jontly optmal value of PU and ED thresholds, lt and δ = {, 2,, N}. Usng smulatons, the optmal thresholds can be stored n a Look-Up-Table (LUT) pror to the deployment of proposed scheduler. Thus the proposed scheme can easly adapt to changng packet arrval rate, packet sze, number of sensor nodes etc. by lookng up and usng the optmal lt, δ for each case. Another novel feature of our scheduler s that we drop PU packets from servce or queue that exceed ther latency deadlne as there s no resultant utlty from servcng such packets. However, droppng them from servce wll reduce congeston and thus reduce latency for packets of all the classes. The proposed scheduler s descrbed n detal n Algorthm. VI. SIMULATION RESULTS In ths secton, we use Monte-Carlo smulatons to evaluate the system utlty performance of our scheduler aganst varous standard schedulng polces such as,, Preemptve prorty schedulng. The smulaton tme T s s set to a large value (4 s) to ensure a steady-state queung behavor. N s set to 5 sensors. Although the proposed scheduler s desgned for 2N PU and ED classes, the smulatons for proposed scheduler becomes computatonally ntractable as N ncreases. Ths s because t requres us to determne 2N jontly optmal latency thresholds 4. Therefore for computatonal tractablty, we assume that half of sensory traffc (.e., 25 sensors) can 4 The number of threshold varables s 2N rather than 2N because the optmal δ for least prorty ED class n.

5 System utlty, V V = System utlty, V V = 3 Prorty to PU [l d, l d 2 ] = [7.8, 8] [a, b, s ] = [5, 9, ] ] = [, 2, ] T pu = T 2 pu = 88 ms γ =. Prorty to PU [l d, l d 2 ] = [4, 8] [a, b, s ] = [,, ] ] = [, 2, ] [T pu ] = [5, 62.5] ms γ =. 5 ED arrval rate, λ ed. 5 ED arrval rate, λ ed Fg. 4. System utlty wth roughly smlar latency requrements of sensors. Fg. 5. System utlty wth dverse latency requrements of sensors. be classfed nto one set of PU and ED class (.e., PU and ED), whle the other half nto PU2 and ED2 class. So, we consder a total of 4 traffc classes. We assume the arrval perod per sensor for PU to be Tpu = 5 ms, whle for PU2 to be Tpu 2 = 62.5 ms. The arrval rate per sensor for ED2 s set to λ 2 ed =.4/ms and for ED t s vared from.4./ms. PLC servce rate s µ = bts/ms. The relatve mportance of all classes s set equal,.e. βpu = βpu 2 = βed = βed 2 =, unless mentoned otherwse. The sze of packets for all classes are set equal to. The latency deadlne for PU s, ld = 4 ms and for PU2 s l2 d = 8 ms. The utlty functon parameters for ED are set to, [a, b, s ] = [,, ] and for ED2 are ] = [, 2, ] unless mentoned otherwse. The latency threshold for ED s, δ = b + (4/a ) and for ED2 s δ 2 =. For each smulaton scenaro, the latency threshold for PU and PU2 class are determned by jontly maxmzng system utlty over lt ld and l2 t ld 2. A. Impact of latency-heterogenety across sensors In ths secton, we study the mpact of ncreasng heterogenety n latency requrements of varous sensors on the performance of dfferent schedulers. Fg. 4 shows plot of system utlty for a nearly homogeneous system wth Tpu = Tpu 2 = 88 ms, [ld, l2 d ] = [7.8, 8] ms, [a, a 2 ] = [5, 7]/ms and [b ] = [9, 2] ms. Then, we ncrease the heterogenety n system by usng the default latency parameters; the resultng system utlty s shown n Fg. 5. We note that the performance gap between the proposed scheduler and the other schemes, V, s much larger for heterogeneous system ( V = 3) compared to homogeneous system ( V = ), especally at hgher λ ed. Ths s because the mpact of prorty schedulng for dfferent PU and ED classes n proposed scheduler becomes more promnent when the traffc classes are dverse. B. Impact of choce of ED threshold, δ Fg. 6 shows the mpact of selectng optmal threshold δ for ED class on the system utlty. We note that the performance of proposed scheduler s sgnfcantly mproved ( V = ) compared to Fg. 5 ( V = 3) where δ was arbtrarly set to b + (4/a ), especally at hgher λ ed. Ths s because selectng optmal δ avods latency of ED2 to becomes very large when λ ed becomes very large relatve to λ ed2. System utlty, V. Prorty to PU [l d, l d 2 ] = [4, 8] [a, b, s ] = [,, ] ] = [, 2, ] [T pu ] = [5, 62.5] ms γ =. 5 ED arrval rate, λ ed V = Fg. 6. System utlty wth optmal selecton of threshold δ. C. Impact of penalzng consecutve PU drops So far, we have assumed there s no penalty for consecutve PU drops,.e., γ =. We now study the mpact of penalzng consecutve PU drops (γ > ) on the performance of dfferent schedulers. Fg. 7 shows the plot of system utlty when the PU drop penalty s small and equal for PU and PU2 (γ = ). We observe that whle the performance of proposed schedulers does not change apprecably, the performance of other schedulers drops down consderably and becomes close to at λ ed = 5. Agan ths s because the proposed scheduler easly adapts to the change n PU penalty by alterng the latency thresholds accordngly. But the other schedulers cannot do so and ther performance suffer. Ths degradaton n performance s more pronounced when the PU drop penalty for hgher prorty class PU s ncreased from γ =.2 to 2 as llustrated n Fg. 8.

6 System utlty, V. Prorty to PU [l d, l d 2 ] = [4, 8] [a, b, s ] = [,, ] ] = [, 2, ] [T pu ] = [5, 62.5] ms γ =.2. 5 ED arrval rate, λ ed Fg. 7. System utlty wth small, equal PU drop penalty (γ =.2). System utlty, V. Prorty to PU [l d, l d 2 ] = [4, 8] [a, b, s ] = [,, ] ] = [, 2, ] [T pu ] = [5, 62.5] ms [γ, γ 2 ] = [2,.2]. 2 4 ED arrval rate, λ ed REFERENCES [] 3GPP, Study on RAN Improvements for Machne-type communcatons, tech. rep., Techncal report, TR , 22. [2] D. Drajc, S. Krco, I. Tomc, M. Popovc, N. Zeljkovc, N. Nkaen, and P. Svoboda, Impact of onlne games and m2m applcatons traffc on performance of hspa rado access networks, n Internatonal Conference on Innovatve Moble and Internet Servces n Ubqutous Computng, pp , July 22. [3] N. Nkaen, M. Laner, K. Zhou, P. Svoboda, D. Drajc, M. Popovc, and S. Krco, Smple traffc modelng framework for machne type communcaton, n Internatonal Symposum on Wreless Communcaton Systems, pp. 5, Aug 23. [4] T. Ta, J. Lu, and M. Shankar, Algorthms and optmalty of schedulng soft aperodc requests n fxed-prorty preemptve systems, Real-Tme Systems, vol., pp , Jan 996. [5] T. Cucnotta, A. Mancna, G. Anastas, G. Lpar, L. Mangeruca, R. Checcozzo, and F. Rusna, A real-tme servce-orented archtecture for ndustral automaton, IEEE Transactons on Industral Informatcs, vol. 5, pp , Aug 29. [6] A. Gotss, A. Loumpas, and A. Alexou, Evoluton of packet schedulng for machne-type communcatons over lte: Algorthmc desgn and performance analyss, n IEEE Globecom Workshop, pp , Dec 22. [7] N. Afrn, J. Brown, and J. Khan, A delay senstve lte uplnk packet scheduler for m2m traffc, n IEEE Globecom Workshop, pp , Dec 23. [8] G. Buttazzo, Hard Real-Tme Computng Systems: Predctable Schedulng Algorthms and Applcatons. New York: Sprnger, Thrd ed., 2. [9] A. Kumar, A. Abdelhad, and T. Clancy, An Onlne Delay Effcent Packet Scheduler for M2M Traffc n Industral Automaton, n Submtted to IEEE Internatonal Systems Conference (SysCon), 26. [] A. Abdelhad and T. Clancy, A Utlty Proportonal Farness Approach for Resource Allocaton n 4G-LTE, n IEEE Internatonal Conference on Computng, Networkng, and Communcatons (ICNC), CNC Workshop, 24. [] A. Abdelhad and T. Clancy, A Robust Optmal Rate Allocaton Algorthm and Prcng Polcy for Hybrd Traffc n 4G-LTE, n IEEE Internatonal Symposum on Personal, Indoor, and Moble Rado Communcatons (PIMRC), 23. Fg. 8. System utlty wth unequal PU drop penalty ([γ, γ 2 ] = [2,.2]). VII. CONCLUSIONS In ths paper, we presented a onlne delay-effcent packet scheduler for uplnk M2M traffc wth heterogenety n latency requrements both wthn and across sensors. The data from each sensor s classfed as ether PU or ED packets. The varyng latency requrements of PU and ED class for dfferent sensors s represented usng dfferent utlty functons. We then proposed a novel proportonally-far mult-class packet scheduler that prmarly gves prorty to ED data as long as the latency deadlne s met for the PU data. However as the sze of networks ncreases, PU packets ncreasngly fal to meet ther deadlnes. We remove the faled PU packets from the system to reduces congeston and thus mprove overall system utlty. We also ntroduce a novel penalty functon as part of PU utlty functon so as to reduce burst PU falures. Usng extensve smulatons, we dd a comparatve analyss of the proposed scheme wth varous state-of-the art schedulng polces such as,, Preemptve prorty etc. We note that as the uplnk traffc ncreases, the proposed scheduler outperforms other schedulers. The performance gap further ncreases wth ncreasng heterogenety n latency requrements and ncrease n penalty for successve PU drops.

7 Algorthm Proposed Onlne Packet Scheduler Inputs ld, l t = {, 2,, N} are latency deadlnes and thresholds for N PU classes. δ = {, 2,, N} are the latency threshold for N ED classes. T sm s the duraton of smulaton and T s the tme resoluton at whch the algorthm operates. Local T c stores current system tme. A and B denotes the set of all PU and ED classes. A e and B e denotes the set of all PU and ED classes that exceed ther correspondng threshold lt and δ respectvely. B denotes the set B B e. A d denotes the set of all PU classes that fal to meet ther deadlnes ld. A h, A e h, B h, B h denote the class wth hghest prorty n sets A, A e, B, B respectvely. z denote class of current packet beng served. Intalzaton Advance current tme T c to be the arrval tme of next packet n system. Set A d =. Set A h, B h from gven set of PU and ED classes. Begn Algorthm: : whle T c T sm do 2: Determne z and the set A d. 3: f A d then 4: Remove the Head-of-Lne (HoL) packet from all PU queues n set A d. go to 5. 5: end f 6: Determne the set A e, B e, B and the classes A e h, B h. 7: 8: f A e & (z / A e (z A e & z A e h )) then Preempt the current packet wth HoL of class A,h. 9: else f A e = & B e = & z B h then : Preempt the current packet wth HoL packet of class B h. : else f A e = & B e & z B h then 2: Preempt the current packet wth HoL of class B h. 3: else No preempton occurs; wat tll current packet leaves server. 4: Advance current tme T c to the servce completon event. 5: Recalculate the sets A e, B e, B and the classes A e h, B h. 6: f A e = & B e = then None of the PU or ED class exceed latency threshold 7: Serve the HoL packet from class B h. 8: else f A e = & B e then None of the PU class exceed latency threshold 9: Serve the HoL packet from class B h. 2: else Some of the PU class exceed latency threshold 2: Serve the HoL packet from class A e h. 22: end f 23: go to. 24: end f 25: T c = T c + T. 26: end whle