(SLA) based scheduling algorithms for wireless networks

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(SLA) based scheduling algorithms for wireless networks

Fig. 1.U 1U 1U Scheduler2TransmitUAntenna2U NSystem block diagramChannel CapacityEstimatora fraction of a time slot, r n . However, in this work, we donot consider the fluid model and assume that a time slot isassigned only to one user. Define Y n (t) asY n (t) ={1 if the scheduler selects user n at time t,0 otherwise.Also, assume that the indictor function, I n (t) is one whenthe queue of user n is non-empty at time t, and zerootherwise.We assume that the link between each user and the basestation is a wireless fading channel. In a power controlledsystem, the average power in each link is maintained at afixed level and the instantaneous power follows a Rayleighfading distribution. The Signal to Noise Ratio (SNR) for then th user is a function of the received power P n , and the noisepower N n . The capacity per unit bandwidth for this user, isgiven byB n = log 2 (1 + P n /N n ). (1)Since thermal noise at each receiver is fixed, the SNR ateach user follows a Rayleigh distribution.We assume that the link capacity is quantized to a limitednumber of levels. Let us assume that the channel capacityfor user n at time t is denoted by g n (t), which is a fractionalnumber. Therefore, the service received by user n at time tis g n (t)Y n (t).Next, we consider two scheduling algorithms. The first oneis proposed to support QoS, and the other one to provide highnetwork throughput.A. Maximum Credit Scheduling (MCS)In order to support QoS, a scheduler monitors and allocatesresources in such a way that users’ effective rates stay withina satisfactory range. A credit based mechanism can be usedto measure and control the service provided to each user;the user n is assigned a credit, denoted by C n (t) (n =1, 2, ··· ,N). A user’s credit represents how much servicethe network owes to the user.The credit for user n at time t evolves as follows:C n (t) =C n (t − 1) + I n (t)r n − g n (t)Y n (t). (2)The second term on the right hand side of the aboveequation, I n (t)r n , represents the service reserved by usern. Ifthen th queue is non-empty, this term is the requestedservice. The third term represents the service received by usern. Starting from C n (−1) = 0 for all users, by induction, itis straightforward to show that 2 leads to the following nonrecursiveexpression for the credits:t∑t∑C n (t) =r n I n (s) − g n (s)Y n (s). (3)s=0s=0In the above equation, the first and second terms arethe reserved and received service by user n up to time t,U Nrespectively. A negative credit means that a user has receiveda better service than what has been reserved. On the otherhand, a positive credit implies that the network owes serviceto the user. Therefore, credit is a measure of how muchservice has been delivered or how much the service providerowes to a user. To support QoS, a scheduler must keep creditsof all the users as small as possible. In this case, for userswith non-empty queues the delivered service is close to theirreserved services.In order to minimize user credits, a Maximum CreditScheduler (MCS) assigns the available bandwidth to the userwith maximum credit [9]; in other words Y n (t) =1only forn = arg max k {C k (t). Since the scheduling is based on thecredit values at time t, and these credits are independent ofthe channel capacities at time t, the total throughput in thisalgorithm is equal to the average channel capacity, E [g n (t)],when E[x] means the expectation of the random variable x.B. Maximum Throughput Scheduling (MTS)It has been proved that to maximize the network throughput,a scheduler must select the user with the best capacity orwith the lowest fading among all the users [5]; , i.e. Y n (t) =1only for n = arg max k {g k (t). The total throughput inthis algorithm is equal to E [max n g n (t)]. However, thisalgorithm has no mechanism for supporting QoS.C. A Trade-off: Throughput versus QoSIn MTS, a user that is trapped in a bad channel state, doesnot receive a service as long as its channel stays at that state.For this user, QoS or SLA is not satisfied. Thus, supportingQoS and maximizing network throughput cannot necessarilybe achieved at the same time.MCS does not face this trade-off in wired networks, sincethe channel responses of all users are equally good, i.e.,g n (t) =1for all n, t. Therefore, by selecting the user withthe highest credit, the scheduler maintains the credits assmall as possible. However, in wireless networks, attemptingto support QoS for users with bad channel response mayresult in reducing network throughput. Another approach isto ignore users with the most eligible QoS that are in deepfade, in favor of users with better channel response with thehope that in the future the capacity of those ignored userswould improve.III. SLA-BASED SCHEDULING ALGORITHMSIn this work, we propose scheduling algorithms that resolvesthe trade-off between throughput and QoS based onthe users SLA. SLA includes QoS, pricing for the serviceprovided and penalty when the agreement is violated. Let usdenote d n (t) to be the income of the service provider fromuser n at time t. Also, let us assume that for the servicereceived by user n, i.e., g n (t)Y n (t), the network charges theuser by α n g n (t)Y n (t), where α n is the rate that the n th userpays for the service. On the other hand, if the user has notreceived the requested QoS, its credit is increased and thenetwork is penalized by f n [C n (t)]. We assume that f n [.]is a real, positive and continuous function with f n [x] =0for x ≤ 0. Bothf n [.] and α n are defined through the SLAbetween the service provider and user n. Thus, we obtain:IEEE Communications Society10290-7803-8533-0/04/$20.00 (c) 2004 IEEE


Seite 3 Donnerstag, 14. Juni 2012Bei der Ortsverwaltung Dingeisdorf ist die Stelle derzum 01.11.2012 neu zu besetzen.VerwaltungsleitungDer Ortsteil Dingeisdorf hat ca. 2.200 Einwohner/innen. Aufgabenschwerpunkteder Verwaltungsleitung sind:• die Vorbereitung der Sitzungen des Ortschaftsrates in Absprachemit dem Ortsvorsteher, der verwaltungsmäßigeVollzug der Beschlüsse des Ort schaftsrates sowie dieBekanntmachung im Gemeindemitteilungsblatt• die Leitung der Ortsverwaltung mit insgesamt 4 Mitarbeiterinnen(1 Verwal tungssachbearbeiterin und 3 Bauhofmitarbeiter)entsprechend den Vorgaben des Ortsvorstehers• die federführende Bearbeitung der Anliegen der Einwohner/innen des Orts teils Dingeisdorf und der sonstigen Aufgaben,die der Ortsverwaltung im all gemeinen Verwaltungsbereichund in Bebauungsplanangelegenheiten über tragensind• urlaubs- und krankheitsbedingte Vertretung z.B. im BereichMelde- und PaßwesenFür diese anspruchsvolle und vielseitige Aufgabe suchen wir eine nMitarbeiter/in mit Sozialkompetenz und mehrjähriger beruflicher Erfahrungin verwaltungstechnischen Aufgaben einer Kommunalverwaltung.Erwartet werden eine abgeschlossene Ausbil dung zumVerwaltungsfachwirt/zur Verwaltungsfachwirtin bzw. das Vorliegender An gestelltenprüfung II. Alternativ ist auch eine langjährige Beschäftigungbei einer Kom munalverwaltung und der erfolgreicheAbschluss der Ausbildung zum/zur Verwal tungsfachangestelltenoder ein vergleichbarer Ausbildungsabschluss ausreichend. DieWohnsitznahme in der näheren Umgebung von Dingeisdorf ist vonVorteil. Der Besitz der Fahrerlaubnisklasse B wäre wünschenswert.Das breite Aufgabenspekt rum erfordert ein hohes Maß anWeiterbildungsbereitschaft und Kommunikationsfä higkeit.Die Stelle setzt Eigeninitiative, sicheres und verbindliches Auftretensowie gute Pe Kenntnisse voraus. Die Stelle ist der Entgeltgruppe 9TVöD zugeordnet. Die Stadt Konstanz fördert die Chancengleichheitvon Frauen und Männern. Bewer bungen geeigneter Frauen sind besonderserwünscht. Fühlen Sie sich durch diese interessante undvielseitige Aufgabe angesprochen, dann reichen Sie bitte Ihre Bewerbungsunterlagenbis 06.07.2012 unter Angabe der Kennziffer205 an die Stadtverwaltung Konstanz, Personalamt, 78459 Konstanz,ein.Telefonische Auskünfte erteilen Ihnen Herr Traber (Tel.: 900-268),Frau Rebholz (Tel.: 900-264) bzw. Herr Pister (Tel.: 07533 5295).1 Trekking-Fahrrad silber1 Kinderanorak grünBürozeiten: Mi und Fr 9.30 - 11.30 Uhr, Do 16.30 - 18.30 UhrTelefon: 44171 Telefax: 943545„Er sagte: Mit dem Reich Gottes ist es so, wie wenn ein MannSamen auf seinen Acker sät; dann schläft er und steht wiederauf, es wird Nach und wird Tag, der Samen keimt und wächstund der Mann weiß nicht, wie.Die Erde bringt von selbst ihre Frucht.“Evangelium: Markus 4, 26-34Samstag 16.06.12 Herz Mariä11.00 Uhr Trauung in St. Marien/Mainauvon Herrn Tobias Nothstein und Frau Sandra Schwenk11. SONNTAG IM JAHRESKREISSonntag 17.06.12 10.45 Uhr Eucharistiefeier mit besonderem Gedenkenfür Herrn Ludwig Allgaier,für Herrn Alfons Kling sowiefür Herrn Harald und Frau Mathilde Dressler (gestifteter Jahrtag)Mittwoch 20.06.12 Mittwoch der 11. Woche im Jahreskreis7.45 Uhr SchülergottesdienstDonnerstag 21.06.12 Hl. Aloisius von Gonzaga18.30 Uhr Heilige MesseSamstag 23.06.12 Samstag der 11. Woche im Jahreskreis12.00 Uhr Trauung in St. Marien/Mainauvon Herrn Christopher Pavel und Frau Sarah Koch14.00 Uhr Trauung mit Brautmesse in St. Marien/Mainauvon Herrn Raphael Werner und Frau Regine Rödigier19.00 Uhr Orgelkonzert


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110.95Total system throughput vs. network load87QoS (minimum assigned relative rate) vs. network loadMTSMCSMPSMIGSIWFQCSDPSSystem throughput0.90.850.80.75MTSMCSMPSMIGSIWFQCSDPSMinimum assigned relative rate654320.710.65Total network loadFig. 2. Throughput vs. network load{ ∞[max E ∑ N]}∑{g} β s {α n g n (s)Y n (s) − f n [C n+1 (s)]} .{Y }s=0 n=1Now, we define G(C(t),Y(t),g(t)) D(t). LetS t ,thestate of the system at time t be defined as the augmentedvector X(t) =(C(t),g(t)). Note that the scheduler knowsthe channel capacities at the decision time, and therefore,the channel capacities are part of the state vector. However,before time t, the vector g(t)) is a random vector. At timet =0the system state is X(0). Then we have[ ∞]J ∗ (X(0)) max E ∑{g} β t G(C(t),Y(t),g(t))|X(0) .{Y }t=0(13)We would like to obtain the optimal policy Y ∗ (t) =µ ( ∗ C(t),g(t) ) at each time slot t that maximizes (13). Wecan rewrite the optimal income in the form of Bellman’srecursive equation for discounted infinite horizon problem atany time slot t [11], as follows:J ∗ (X(t)) = max {G(C(t),Y(t),g(t))Y (t)[+ βE g(t+1) J ∗ (C(t +1),g(t + 1)) ] }.If we denote the probability of g(t+1) = g k by ˆp g k, whereg k is the k th level quantized value for the channel capacity,we obtain:J ∗ (X(t)) = maxY (t) {G(C(t),Y(t),g(t))+ β ∑ kˆp g kJ ∗ ( C(t +1),g k) }. (14)Starting from X(t), the scheduler selects the user thatmaximizes the righthand side of (14), in which the firstterms represents the current income (as seen in the greedyalgorithm, MIGS) and the second term represents the incometo-go.It can be shown that this maximization is equivalent toselecting the user n in the following maximization problem:max {α ng n (t)+f n [C n (t)+r n ] − f n [C n (t)+r n − g n (t)]n⎡ ⎤0+ β ∑ .ˆp g kJ ∗ (C(t)+r −⎢ g n (t)⎥k⎣ . ⎦ ,gk )}.0Fig. 3.Fig. 4.00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Total network loadMinimum assigned relative rate vs. network loadTotal system incomeSystem income vs. network load10510−1−2MTSMCS−3MPSMIGSIWFQCSDPS−4−50.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 12 x Total network loadTotal income vs. network loadIV. SIMULATIONS RESULTSIn order to evaluate the performance of our algorithms, wehave simulated a single-cell wireless system where users arerandomly distributed. We assume that path loss and shadowfading are compensated by a power allocation mechanismand the channel follows a Rayleigh fading distribution. Byconsidering the same noise level at all receivers, the receivedsignal power also follows a Rayleigh distribution. Here wehave assume that number of quantized levels of channelcapacities is Q =4. These levels and their probabilities are{1.0, 0.6, 0.4, 0.2} and {0.43, 0.24, 0.19, 0.14}, respectively.If R n is the assigned rate to user n, and r n is the reservedrate by that user, we define the minimum assigned relativerate over all users as η = min n { Rnr n}. This value can beconsidered as a measure of QoS; to support QoS for all users,we want η ≥ 1.First we present the simulation results for MIGS andcompare its performance with MTS, MCS, MPS, IWFQ, andCSDPS for a system with four users. The reserved rates ofthe four users are ρ[0.1, 0.2, 0.3, 0.4], where 0 ≤ ρ ≤ 1 isthe network load. Also, we assume that α n = 1000 for allusers.Throughput, minimum assigned relative rate, and totalincome are plotted in Figures 2-4, respectively. The penaltyfunction in the simulations is selected as in (5) with γ n =1.The horizontal axis in all these figures shows the networkload. As illustrated in Figure 2, MTS and MIGS achieve themaximum throughput (the expectation of maximum link capacity,E{max(g) =0.96}). MCS achieves a flat throughputwhich is equal to the average link capacity (E(g) =0.68).At low network loads, MPS tries to satisfy each user withIEEE Communications Society10310-7803-8533-0/04/$20.00 (c) 2004 IEEE


0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10.9Throughput vs. Total reserved rate13Total Income vs. Total reserved rate120.8511Throughput0.80.75Total Income109Fig. 5.0.70.65Total reserved rateMPSMIGSMIDPSThroughput of MIDPS, MIGS, and MPS vs. network loadMinimum assigned relative rate1.0510.950.90.850.80.750.70.65Minimum assigned relative rate vs. Total reserved rateMPSMIGSMIDPS0.60.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1Total reserved rateFig. 6. Minimum assigned relative rate of MIDPS, MIGS, and MPSvs. network loadits requested bandwidth; that is, throughput is minimallyallocated to satisfy each user. As network load increases, thesystem throughput increases and it approaches to that of MTSand MIGS. As illustrated in Figure 3, at low network loadsall the algorithms support QoS. However, as network loadincreases, MPS and MIGS try to maintain QoS for all users,while MTS and CSDPS fail to do so. This result is expectedsince they are not designed to provide QoS. Since MCSdoes not utilize bandwidth as efficiently as MIGS, it failsat high network loads due to the lack of available channelbandwidth. As it was mentioned earlier, total income is acombination of system throughput and penalty when QoSrequirement is not met. This quantity is shown in Figure 4.MIGS generates the highest income since the throughput andpenalty are optimized jointly. The income for MTS, MCS,IWFQ, and CSDPS drop at high network loads, since theyfail to meet QoS after certain loads. MTS and CSDPS failto meet QoS at lower network loads compared to MCS andIWFQ, and thus, their incomes drop faster. Total income forMPS increases as load increases, since it tries to minimizepenalty independent of load, while at large loads, throughputgrows and increases the income. At high network loads, MPSincome approaches that of MIGS, since both achieve similarthroughput at high loads.Next, we evaluate the performance of MIDPS and compareit with performance of MIGS and MPS (See Figures 5, 6 and7). However, because of complexity issue of DP algorithm,we consider only three users, limit the credits of users to bebetween -1 and 2, and perform the simulations for three caseswhere the reserved rates are a:[0.2, 0.2, 0.2], b:[0.2, 0.2, 0.4],and c:[0.2, 0.2, 0.6]. The penalty function is described by (5),and α 1 =1, α 2 =2, and α 3 =4. Figures 5 and 6 show thatFig. 7.87MPSMIGSMIDPS60.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1Total reserved rateIncome of MIDPS, MIGS, and MPS vs. network loadthe system throughput and QoS with MIDPS are as good asthe throughput and QoS with MIGS. Therefore, MIDPS cansupport QoS and provide high system throughput. However,as shown in Figure 7, the total income with MIDPS is betterthan the sub-optimal MIGS. We have to mention that whenwe increase the range of credits, sub-optimal solution MIGSperforms close to the optimal solution MIDPS.V. CONCLUSIONIn this work we have proposed Service Level Agreement(SLA) based scheduling schemes. We have introduced anotion of income maximization where throughput is the objectiveof maximization with the constraint that the scheduleris penalized when the QoS or SLA is violated. We haveproposed a greedy approach and a dynamic programmingapproach to solve the problem. Our results show that theperformance of the algorithm is superior to cases where onlythroughput or QoS is considered in the scheduling process.REFERENCES[1] R. Guerin, H. Ahmadi, and M. Naghsineh, ”Equivalent capacityand its application to bandwidth allocation in high-speed networks,”IEEE Journal of Selected Areas in Communications,, Vol. 9, No. 7,September 1991.[2] P. Bhagwat, A. Krishna, S. Tripathi, ”Enhancing Throughput overWireless LANs Using Channel State Dependent Packet Scheduling,”Proc. INFOCOMM96, March 1996, pp. 1133-1140.[3] C. Fragouli, ”Controlled multimedia wireless link sharing via enhancedclass-based queuing with channel-state dependent packet scheduling,”Proceedings of INFOCOM’98, Vol. 2, March 1998, pp. 572-580.[4] Yaxin Cao, Victor O. K. Li, Zhigang Cao, ”Scheduling Delay Sensitiveand Best-Effort Traffic in Wireless Networks,” ICCC 2003,[5] M. Grossglauser, D. Tse, ”Mobility Increases the Capacity of WirelessAdhoc Networks,” IEEE INFOCOMM01, April 2001.[6] Dapeng Wu, Rohit Negi, ”Utilizing Multiuser Diversity for EfficientSupport of Quality of Service over a Fading Channel,” ICCC 2003,[7] S. Lu, V. Bharghavan, ”Fair Scheduling in Wireless Packet Networks,”IEEE/ACM Trans. Networking, Vol. 7, No. 4, pp. 473-489, 1999.[8] Xin Liu, Edwin K. P. Chong, Ness B. Shroff, ”Opportunistic TransmissionScheduling With Resource-Sharing Constraints in WirelessNetworks,” IEEE Journal of Selected Areas of Communications, Vol.19, No. 10, pp 2053-2064, Oct. 2001.[9] A. C. Kam, K. Y. Siu, ”Linear Complexity Algorithms for BandwidthReservatations and Delay Guarantees in Input Queued Switches withno Speedup,” Proc. International Conference on Network Protocols 98,Austin TX, Oct. 1998, pp. 2-11.[10] M. Olfat, ”Spatial Processing, Power Control, and Channel Allocationfor OFDM Wireless Communications,” phD Thesis, November 2003.[11] D. P. Bertsekas, ”Dynamic Programming And Optimal Control,”Athena Scientific, 1995.IEEE Communications Society10320-7803-8533-0/04/$20.00 (c) 2004 IEEE

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