Distributed Scheduling and Power Control for Predictable IoT Communication Reliability

Dstrbuted Schedulng and Power Control for Predctable IoT Communcaton Relablty Lng Wang and Hongwe Zhang Department of Electrcal and Computer Engneerng Iowa State Unversty {lngw, hongwe}@astate.edu Pengfe Ren Department of Computer Scence Wayne State Unversty fl286@wayne.edu Abstract Msson-crtcal IoT applcatons such as wrelessnetworked ndustral control requre relable wreless communcaton. Due to co-channel nterference and wreless channel dynamcs (e.g., mult-path fadng), however, wreless communcaton s nherently dynamc and subject to complex uncertantes. Jont schedulng and power control has been explored for relable wreless communcaton, but exstng solutons are mostly centralzed or do not consder real-world challenges such as fast channel fadng. Towards a foundaton for msson-crtcal IoT communcaton, we develop a dstrbuted, feld-deployable approach to jont schedulng and power control that adaptvely regulates cochannel nterference and ensures predctable IoT communcaton relablty n the presence of wreless communcaton dynamcs and uncertantes. Our approach effectvely leverages the Perron- Frobenus theory, physcal-rato-k (PRK) nterference model, and feedback control for PRK model adaptaton and transmsson power update. Through smulaton analyss, we have shown that our approach mproves concurrency by 7% than state-of-art fxed schedulng whle ensurng successful SINR trackng over tme. To the best of our knowledge, our approach s the frst dstrbuted schedulng and power control scheme that ensures predctable wreless communcaton relablty whle consderng real-world challenges such as fast channel fadng, and t s expected to serve as a foundaton for real-world deployment of msson-crtcal IoT systems. I. INTRODUCTION Wreless networks are steppng nto a new era from humanorented cellular networks to ubqutous IoT. The emergence of IoT s changng our vson for future wreless networks. Wreless network standards such as ISA1.11a and WrelessHART [1] have facltated applcatons of IoT n ndustral automaton, home ntellgence, and health care. Whle those standards try to mprove wreless communcaton relablty through mechansms such as graph routng [2] and packet retransmsson, ther sacrfce n channel spatal reuse and system capacty have mpeded at-scale deployments of IoT. In the meanwhle, Petersen and Aakwag [3] have verfed that wreless nstrumentaton for safety-crtcal applcatons n ol and gas ndustry are stll confronted wth a serals of ssues such as weak RF sgnals, nterference, and multpath fadng [4]. Furthermore, wreless networks n the current IoT practce under star and mesh topologes wll nevtably suffer from ncreased co-channel nterference from close-by lnks as network traffc ncreases and as network scales up. These ssues call for new network desgns to enhace the relablty and capacty of wreless networks for mssoncrtcal applcatons. Uncertantes of wreless networks manly come from cochannel nterference and channel dynamcs (e.g., due to shadowng and mult-path fadng). It s undoubtable that redundant desgns such as graph routng and packet retransmsson can mprove network relablty to some extent, but they cannot elmnate packet loss from wreless network uncertantes. Whle cellular networks mtgate co-channel nterference through mechansms such as cell dvson, CDMA, and TDMA [], current IoT systems have mplemented lmted strateges to address co-channel nterference. The lmtatons of tradtonal CSMA mechansm have propelled the adopton of TDMA n IEEE 82.1.4-based standards [6]; however, current IoT systems ncludng ISA1.11a and WrelessHART only allow one user at each tme slot and frequency or allocate dedcated tme slots to avod nterference, under whch system capacty s underutlzed and would potentally lead to nablty of hgh data-rate and delay-senstve applcatons such as realtme control. Therefore, mproved TDMA schedulng wll be desrable. In addton, pror research has confrmed that power control can mprove system capacty [4], and many studes have showed the benefts of jont power control and schedulng as well [7][8]. Unfortunately, dstrbuted TDMA schedulng and power control s challengng due to the NPhardness of optmal schedulng and the fact that there may not always exst a feasble power assgnment for every set of concurrent transmssons. Moreover, despte feld experments n [9] evdence that the receved sgnal strength across lnks of wreless sensor networks changes over tme and suggeste that adaptve power control s requred to compensate tmevaryng channel attenuaton, many of the exstng work on jont schedulng and power control n IoT have overlooked channel dynamcs and assumed constant channel gan. In ths paper, we am to develop a feld-deployable, jont TDMA schedulng and power control framework for supportng relable wreless networks n IoT systems. Ths framework s desgned to mplement dstrbuted schedulng and power control wth an objectve of maxmzng concurrency and trackng SINR over channel dynamcs. We dved nto the Perron-Frobenus theory [1] and formulated our problem. We adopted Physcal-Rato-K (PRK) nterference model [11] and NAMA TDMA schedulng algorthm [12] to buld the whole

dstrbuted framework whle both were specfcally desgned to facltate dstrbuted schedulng. We employed feedback control mechansm to adapt schedulng K and transmsson power by current schedulng K and SINR measurement. In a slowly tme-varyng system, the schedulng K wll be expected to change at a large tme-scale whle transmsson power wll be updated probably at each tme slot depng on the scale of channel varaton. We evaluated our framework and algorthms, and the smulaton results demonstrated sgnfcant mprovement n concurrency and successful trackng of target SINRs. To the best of our knowledge, the proposed scheme n ths paper s the frst one that can satsfy SINR requrement toward channel dynamcs wthout sacrfce n concurrency. Ths fundamental desgn wll pave the way for future feld deployment of IoT as the development and penetraton of IoT expands to a large scale. The remanng parts of ths paper are organzed as follows: Secton III defnes the system model and dentfes the problem; Secton IV elaborates on the framework and algorthms; Secton V evaluates the desgn; Secton II hghlghts related work and fndngs; Secton VI concludes the paper. II. RELATED WORK Foschn and Mljanc s work n [13] has been wdely consdered as a canoncal algorthm n the feld of power control. Ths smple, autonomous, and dstrbuted power control, where each lnk updates ther transmsson power only from ther receved SINR, was proved to converge to a unque fxed pont at whch the total energy consumpton s mnmzed under SINR constrants. Debass Mtra [14] exted the Foschn and Mljanc s algorthm and verfed the asynchronous convergence. Bambos et al. [1] and Huang et al. [16] have consdered fxedstep power adjustment algorthms for admsson control, but those algorthms do not ensure convergence to the fxed pont. Yates [17] proposed concepts of standard nterference functon and standard power control and reveals the convergence condtons for general power control algorthms. Whle Foschn and Mljanc s algorthm has guded the study on dstrbuted power control, most lterature has overlooked the feasblty condton for power control. Gupta et al. [18] nvestgated the system capacty lmtaton from co-channel nterference and concluded that when dentcal randomly located nodes, each capable of transmttng at W bts per second, form a wreless network, the throughput for each node can asymptotcally approach. Ths fndng ndcates that mtgatng co-channel nterference by optmally utlzng power control and schedulng s requred n wreless networks. Elbatt and Ephremdes [7] ntroduced jont schedulng and power control framework to address multple access ssue n wreless ad hoc networks, yet ted to be mplemented n a centralzed way. Wan et al. [8] further suggested that the cumulatve co-channel nterference beyond a certan range can be upper bounded under the lnk-lengthbased path loss law and drected the schedulng ssue nto selectng a maxmum set of ndepent lnks. Che et al. [19] and Wan et al. [8] proposed approxmate algorthms n obtanng the maxmum set of ndepent lnks. Magnús M. Halldórsson conducted extensve research on jont schedulng and power control. Partcularly, Magnús M. Halldórsson [2] proposed to dvde all lnks nto equal lnk-length group and allocate transmsson power for each group; the algorthm s centralzed and does not consder channel dynamcs, thus unsutable for dstrbuted schedulng and power control n realworld networks of fast-varyng channel gans. Ln et al. [9] has evdenced n feld tests that the channel for wreless sensor networks changes over tme and adaptve transmsson power s requred. Ther work, however, dd not consder jont schedulng and power control to ensure recever-sde SINR all the tme. Hollday et al. [21] proposed adaptve power control wth channel dynamcs to converge to a fxed pont. However, ther algorthm also dd not consder jont schedulng and power control, and t only works for a set of lnks for whch there exst a feasble power assgnment. Kandukur and Boyd [14] proposed optmal power control n nterference-lmted fadng wreless channels wth outage-probablty specfcatons. Chang et al. [22] exted Kandukur and Boyd s work and proposed dstrbuted power control scheme to converge to the optmal transmsson power. Those algorthms, however, only try to ensure avearge packet delvery rate wthout consderng per-packet SINR assurance. Zhang et al. proposed the PRK nterference model [11] and a control-theoretc approach to PRK-based schedulng [23] for predctable mean communcaton relablty. However, ther desgn has only consdered schedulng wthout consderng jont schedulng and power control for predctable nstantaneous communcaton relablty. III. SYSTEM MODEL AND PROBLEM FORMULATION Gven a set of lnks n wreless sensor networks, each lnk s recever wll receve sgnals from other lnks sers due to broadcast nature of electromagnetc wave. The receved sgnals from other lnks are called co-channel nterference. Accordng to the SINR model, a lnk would transmt a packet successfully f and only f p G j p jg j + n β th (1) where p s lnk s transmsson power; G s lnk s channel gan; G j s the channel gan from lnk j s ser to lnk s recever; n s lnk s recever-sde thermal nose; β th s lnk s target SINR. We assume all lnks have the same target SINR. As shown n (1), ndvdual lnk s SINR deps on other lnks transmsson power. Transform all lnks SINR requrements nto matrx form. We have where F j = P F P + η (2) { β th G j /G, f j, f = j

and η = β th n /G Here P s the varant, and F s normalzed gan matrx. Inequalty (2) can be regarded as a Lnear Programmng ssue [24]. Under constrant P >, a soluton of transmsson power exts f and only f (2) s feasble. On the contrary, f P, the problem can be converted nto jont schedulng and transmsson power where all nfeasble lnks transmsson power would be. A. Perron-Frobenus theory and feasblty Theorem 1. (Perron-Frobenus Theory [2]) If A s a square non-negatve matrx, there exsts an egenvalue λ such that λ s real and non-negatve; λ s larger or equal to any egenvalue of A; there exsts an egenvector x > such that Ax = λx. Lemma 1. (Feasblty condton [1]) A set of lnks s feasble f and only λ(f ) 1 when η = and λ(f ) < 1 when η. Lemma 2. (Optmum power [1]) If a set of lnks s feasble, the optmum power s P = (F I) 1 η. In Lemma 1, λ(f ) s the the largest egenvalue of F, called Perron root. P s called fxed pont. Lemma 1 can be proved as n [1] when transformng Inequalty (2) nto (F I)P > η. Accordng to the feasblty condton n Lemma 1, two lnks are nfeasble f β 2 th G 12G 21 > G 11 G 22. It s obvous that two close-by lnks are easly becomng nfeasble under constant path loss law only f the nterferng lnk length s shorter than sgnal lnk length. Ths s consstent wth the requrement for schedulng n real systems. Th Perron-Frobenus theory not only suggests the exstence of nfeasblty for a set of lnks but also ndcates that a subset of lnks can be feasble f λ(f s ) < 1 under thermal nose, where F s s the matrx correspondng to a subset of lnks. In ths sense, we defne a maxmal feasble subset, called MFS as a subset nto whch the addton of any one more lnk wll make t nfeasble. Furthermore, we denote all maxmal feasble subsets as an unon U = {S 1, S 2,..., S m } (3) and ther correspondng optmal power as P = {P 1, P 2,..., P m} (4) In the best case, all scheduled lnks at each tme slot are expected to be a MFS and transmt wth optmal power so as to maxmze concurrency and guarantee relablty. However, fndng these maxmal feasble subsets are known as NP-hard. Even n a centralzed scheme n whch all lnks channel nformaton are known, t s almost nfeasble to obtan the MFS and ther optmal transmsson power n reasonable computaton tme, not to menton that wreless ad hoc networks are ted to be dstrbuted. Therefore, we need to fgure out a smple way to dentfy feasble lnks and remove nfeasble lnks. B. Pyscal-Rato-K (PRK) model and feasble schedulng K The physcal-rato-k(prk) model [11] s an nterference model that defnes the conflct relatonshp between two lnks. In other words, ths model determnes whether two lnks can transmt at the same tme or not. Accordng to the PRK model, a lnk j conflcts wth a lnk f G j G K () We fnd that the parameter K of the PRK model s drectly related to the feasblty of gan matrx F. For each lnk, a gven K would dvde all lnks nto conflctng lnks and concurrent non-nterferng lnks. If K s too large, most lnks wll be regarded as conflctng lnks and sacrfce concurrency; f K s too small, the concurrent lnks are not necessarly non-nterferng. Thus fndng the exact K s very mportant. Defnton 1. The feasble K for lnk, denoted by Kf, s the mnmum K such that all lnks satsfyng G j G can Kf transmt wth lnk at the same tme under optmum power. Out of all MFSs, we represent all the MFSs that nclude as U = {S 1, S 2,..., S m } (6) and correspondng transmsson power as P = {P 1, P 2,..., P m }. (7) The lnks n U are those lnks that can transmt at the same tme as, denoted by N. By the defnton of Kf, we have Kf G = mn (8) j N G j We can prove that Kf s the mnmum K for lnk, that s, the mnmum boundary that dvdes concurrent lnks and conflct lnks. If we have K < Kf, there must exst a lnk whch satsfes G j = G /K and s allowed to transmt at the same wth lnk. However, t s not among concurrent lnks snce G j = G /K > G /Kf. Allowng ths lnk to transmt smultaneously would not guarantee feasblty. Smlarly, lettng K > Kf wll mss some concurrent lnks. Therefore, Kf s the mnmum value under optmum power. Once we fnd the feasble K for each lnk and buld conflct relatonshp, we can use NAMA schedulng [12] to select concurrent lnks. NAMA schedulng s a dstrbuted approach to channel access schedulng for wreless ad hoc networks. Based on known conflct relatonshps, each lnk calculated a prorty for tself and all ts conflct lnks. A lnk would get access to the channel f t has the hghest prorty among all ts conflctng lnks. The prorty s calculated as follows p t = Rand(k t) t, k M (9) where M s a set of lnks that conflct wth lnk. Therefore, back to feasblty condton and PRK model, to ensure relablty becomes fndng the feasble K and optmum transmsson power for each lnk. Under channel dynamcs,

feasblty condton would change and schedulng K(.e., the parameter K of the PRK model) may change as well. The next secton wll present how the system converges to an near-optmal K and feasble transmsson power over channel varatons. IV. DISTRIBUTED SCHEDULING K AND POWER CONTROL In ths secton, we present a dstrbuted framework to obtan near-optmal schedulng and power control. Ths framework conssts of the channel measurement module, NAMA schedulng module, SINR measurement module, and PRK adaptaton and transmsson power update module. For slowly tmevaryng IoT systems, the channel measurement module wll measure average channel at setup stage and update t at a long tmescale. All packets are sent n the data channel. At each tme slot, each ser wll run NAMA schedulng to determne f t can obtan channel access or not. When a ser gets the channel access, t wll s a packet, and ts recever wll then measure current SINR and s t back to the ser va acknowledgement packet. So the whole system requres ACK feedback. When the ser receves current SINR, t wll calculate the schedulng K and transmsson power for the next tme slot accordng to current K, transmsson power and SINR. Ths dstrbuted framework wll run as shown n Algorthm 1. Input: P 1, K1, β th Output: p t, xt Ḡ,j = MeasureAverageChannel(); for t 1 to T do x t = NAMASchedulng(kt, Ḡ,j ); β t = MeasureSINR(pt, xt ); (p t+1, k t+1 ) = UpdateSchedulngKandPower(p t, kt, β t, β th); Algorthm 1: Dstrbuted schedulng K and power control The core part of ths framework s updatng schedulng K and transmsson power. To update schedulng K and transmsson power, we use teratve approach based on feedback mechansm. Snce t s challengng to acheve the exact target SINR and also not necessary, we set a tolerance area as SINR target regon, [β th, Uβ th ], to tolerate any slght varaton. We set a reference nterval [K lref, K rref ]. Specfcally, K lref = β/(1+1/u) and K rref = β/(1 1/U). Despte not all lnks feasble K are bound n the reference nterval [K lref, K rref ], t s a desrable nterval for each lnk consderng feasblty condton. Lmtng all lnks K n ths nterval would lose a lttle bt concurrency but the strategy of regulatng all lnks nterference n a range would keep a balanced nterference among lnks and mantan a stable system. The K reference nterval and SINR target regon dvde K SINR plane nto multple regons as shown n Fgure 1. We update K and transmsson power by ths plane. To decouple the nteractve mpact of schedulng and power control, we Uβ β SINR decrease power K lref ncrease K K rref decrease K Increase power Fg. 1. The plane of schedulng K and SINR. Transmsson power and K wll be adjusted by ther current locaton n the plane. frst change K under both overshoot and undershoot of SINR. The rules are as follows: Case 1. In case that the current SINR s greater than SINR margn Uβ th, f K > K rref, the schedulng K should be decreased; otherwse, keep K unchanged and decrease transmsson power. Case 2. In case current SINR s smaller than target SINR β th, f K < K rref, schedulng K should be ncreased; otherwse, transmsson power should be ncreased. The algorthm s as descrbed n Algorthm 2. We explan how to calculate k t+1 and p t+1. If β t > Uβ th and k t > K rref, we thnk k t can be further decreased to tolerate more nterference wth a beneft n mprovng concurrency. Expectng β t+1 = β th, we have I t + I t+1 = p t+1 G /β th (1) where I t+1 are allowed nterference ncrease from decreasng K. Further, I t /G + j s t+1 K p t+1 j /k j = p t+1 /β th (11) where k j = G /G j and s t+1 s the set of all newly-added lnks satsfyng k j k t+1. Because t s dffcult to obtan the set s t+1 and know each lnk s transmsson power, we further relax (11) to I t /G + p t+1 /k t+1 = p t+1 /β th (12) Let I t/g = p t /βt and γ t = β th /β t, we obtan kt+1 = 1/(1 γ t)β th. Snce we don t hope k t+1 changes too much at each tme slot to cause system oscllaton, we lmt k t+1 k lref. It s worthwhle to note that k t+1 s an approxmate value. Further adjustment may be needed before convergng to a fxed value. If β t > Uβ th but k lref < k t < k rref, we thnk K s wthn reference range and doesn t need to change, we only reduce power to satsfy β t+1 = Uβ th. Specfcally, square root power

control s adopted to avod large transmsson power change. If β th < β t < Uβ th but k lref < k t < k rref, K and transmsson power wll keep unchanged at the next tme slot. Once a few lnks settle down and mpact on other lnks don t change, the whole system wll start to converge. In addton, we control the range of power ncrease at each tme step so as to reduce the settle-down lnks to become unstable. We can use the same approach above to obtan k t+1 = 1/(γ t 1)β th when k t < k rref. If the actual ncreased k t+1 s larger than K rref, we wll further ncrease transmsson power to ensure expected SINR, M = U/2. Let Replace k t+1 I t /G p t /k t+1 = K rref, we get p t+1 = M K rref β t K rref = pt+1 (13) Mβ th β th β t p t (14) For wreless sensor networks, SINR overshoot may be acceptable but undershoot s not desrable. So we attempt to satsfy SINR requrements rght away by schedulng and further power control when schedulng doesn t work n the case the lnk gan tself s very small. Input: k t, βt, pt, β th Output: p t, kt γ t β th β t f γ t < 1/U then f k t > K rref then k t+1 1 max( β 1 γ t th, K lref ) else p() max( pt U, Uγ t pt ) p() = max(p(), P mn ) p() = mn(p(), P max ) f γ t > 1 then f k t < K rref then k t+1 1 γ t 1β th f k t+1 >= K rref then p t mn(upt, M K rref β t K rref γ tpt ) k t+1 K rref else p t mn(upt, Mγ tpt ) p t = max(pt, P mn) p t = mn(pt, P max) Algorthm 2: Update Schedulng K and Transmsson Power The whole system s expected to keep schedulng K constant or change slowly. In the case there s no channel dynamcs, schedulng and transmsson power converge to fxed value. The SINR regon can be used to tolerate nterference varaton from random NAMA schedulng. Once varatons from channel dynamcs are over the system tolerance level and make lnks nfeasble, the system wll recalculate schedulng K and transmsson power. V. SIMULATION RESULTS In ths secton, we verfy the convergence property of the whole framework and algorthms, and evaluate recever-sde SINR varaton and concurrency n networks. We use Matlab to smulate a network n a rectangle area wth network node densty λ, where all sers are randomly and unformly dstrbuted and ther recevers are around the sers wth a random dstance between d mn and d max. The traffc model s full-buffer model, whch means packets are always ready to transmt f they get a chance to access the channel. Constant channel and dynamc channel wth Raylegh multpath fadng are smulated separately. Maxmum transmsson power and mnmum transmsson power s dbm and - 1dBm, respectvely. The channel attenuaton s n the range [ 7dB, 12dB]. Each tme slot s allocated ms. All smulaton parameters are showed n Table I. TABLE I SIMULATION PARAMETERS Symbol Parameter Default value W Network wdth 1 m L Network length 1 m λ Network densty. d mn Mnmum lnk length m d max Maxmum lnk length 1 m α Path loss exponent 3. µ h Raylegh fadng mean db n Thermal nose -99 dbm β th Target SINR db P max Maxmum transmsson power db P mn Mnmum transmsson power -1 db P Intal transmsson power db U SINR margn 2 T Tmeslot duraton ms A. Convergence property Set the default SINR margn U = 2, we have K lref = 2/3β th, K rref = 2β th. Startng wth K = 3β th and P = dbm, we frst observe how schedulng K, transmsson power, and SINR change wth constant channel. Fg. 2 shows that schedulng K for each lnk wll be fxed around tme slots, and Fg. 3 shows that power control wll converge to fxed value around 1 tme slots. These results are as expected whle our desgn has lmted the adjustment range of transmsson power at each tme slot to obtan a stable system. As n Fg. 6, all lnks SINR s over the target value. Ths suggests that our desgn ensures trackng and satsfacton of the requred target SINR.

Schedulng K 1 9 8 7 6 4 3 2 1 Schedulng K change over tme lnk1 lnk2 lnk3 lnk4 lnk lnk6 lnk7 lnk8 lnk9 lnk1 lnk11 lnk12 lnk13 1 2 3 4 6 7 8 9 1 Tme slots, t over the same network nstantaton under constant channel and Raylegh fadng. We can see the dfference where SINR has ncreased and t s a result from transmsson power adjustment. Transmsson power (dbm) - Transmsson power varaton over dynamc channel lnk1 lnk2 lnk3 lnk4 lnk lnk6 lnk7 lnk8 lnk9 lnk1 lnk11 lnk12 lnk13 Fg. 2. Schedulng K converges to a fxed pont for each lnk Transmsson power, p(dbm) - Transmsson power change over tme(dbm) lnk1 lnk2 lnk3 lnk4 lnk lnk6 lnk7 lnk8 lnk9 lnk1 lnk11 lnk12 lnk13-1 2 4 6 8 1 Tme slots, t Fg. 3. Transmsson power converges to a fxed pont for each lnk B. Adaptaton to dynamc Channels We model the wreless channel as slowly tme-varyng channel. Each lnk s channel gan at current tme slot s the average value over channel gans of a few prevous tme slots and a random Raylegh fadng. The number of depent slots s set as W = 2. Fg. 4 ndcates that channel varaton s around 2dB. Under ths level of channel dynamcs, schedulng K s mostly the same as constant channel for the same nstance of smulated work, so here we just present the varaton of transmsson power. As shown n Fg. 4, for some lnks, transmsson power s adjusted due to channel dynamcs and then keep stable. Fg. 6 and Fg. 7 are the SINR varaton -1 2 4 6 8 1 Tme slots, t Fg.. Power update for each lnk over Raylegh fadng SINR over target (db) SINR change over tme(db) 2 1 1-1 2 3 4 6 7 8 9 1 Tme slot, t Fg. 6. SINR varaton for each lnk under constant channel SINR over target, db SINR change over tme(db) 2 1 1-1 2 3 4 6 7 8 9 1 Tme slots, t -69-69.2 Fg. 7. SINR varaton for each lnk under Raylegh fadng -69.4 Channel gan (db) -69.6-69.8-7 -7.2-7.4-7.6-7.8-71 1 2 3 4 6 7 8 9 1 Tme slots, t Fg. 4. Instantaneous channel gan over tme slots under Raylegh fadng C. Concurrency Concurrency s the man performance we care about. We compare our schemes wth optmal schedulng and power control and other two typcal and state-of-art approaches. ALOHA schedulng wth Fractonal power control. ALOHA schedulng s random schedulng. Each lnk has equal chance to transmt or not. For fractonal power control [26], each lnk updates ther transmsson power by ther nstantaneous channel gan, P t+1 = P / G.

NAMA schedulng wth suffcent K and FM control. We calculate a suffcent K for each lnk at the frst tme slot. Ths suffcent K wll ensure all non-conflctng lnks are feasble under constant power. We then run classcal Foschn and Mljanc s dstrbuted power algorthm [13], P t+1 = β th β t P t. Optmal schedulng and transmsson power. CPLEX s an optmzaton tool. We transform (1) nto mxed nteger lnear programmng ssue and obtan the maxmal number of feasble lnks and ther transmsson power gven the constant gan matrx of a set of lnks. Rato of feasble lnks to total lnks.6..4.3.2.1 Aloha & Fracton power NAMA & FM power Proposed scheme Optmal schedulng & power Fg. 8. Comparson of rato of concurrent lnks over total lnks We run each scheme tmes and get the average value. Fg. 8 suggests that gven a random network, nearly 6% lnks can transmt smultaneously under optmal transmsson power. ALOHA schedulng has the least number of feasble lnks, whch verfes the mportance of well-regulatng schedulng. Compared to NAMA schedulng wth effcent K, our proposed scheme mproves concurrency by 7%. Ths result ndcates the beneft of adaptve schedulng. VI. CONCLUSION In ths paper, we has amed to leverage schedulng and power control to support relable IoT applcatons. Specfcally, we have focused on ensurng hgh concurrency whle guaranteeng applcaton-requred communcaton relablty. We have adopted the PRK nterference model and NAMA schedulng and proposed our schedulng K and power control framework. We have conducted experments and verfy that ths framework enables dstrbuted convergence n jont schedulng and power control wth advantages n the ease of mplementaton, sgnfcant mprovement n concurrency and SINR guarantees. The proposed framework s expected to serve as a foundaton for dstrbuted schedulng and power control as the penetraton of IoT applcatons expands to scenaros where both the network capacty and communcaton relablty becomes crtcal. REFERENCES [1] M. Nxon and T. 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