Optimal server assignment in multi-server queueing systems with random connectivities

In this paper, we provide complementary results on delay-optimal server allocation in multi-queue multi-server (MQMS) systems with random connectivities. More specifically, we consider an MQMS system where each queue is limited to get service by at most one server during each time slot. It is known that maximum weighted matching (MWM) is a throughput-optimal server assignment policy for such a system. In this paper, using dynamic coupling argument we prove that for a system with i.i.d. Bernoulli arrivals and connectivities, MWM minimizes, in stochastic ordering sense, a range of cost functions of the queue lengths such as total queue occupancy (which implies minimization of average queueing delay). Finally, we propose a low complexity heuristic server assignment policy for MQMS systems namely least connected server first/longest connected queue (LCSF/LCQ) and through simulations we show that it performs very closely compared with the optimal policy in terms of average queueing delay.

[1]  Marco Ajmone Marsan,et al.  Bounds on average delays and queue size averages and variances in input-queued cell-based switches , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[2]  Nick McKeown,et al.  A Starvation-free Algorithm For Achieving 100% Throughput in an Input- Queued Switch , 1996 .

[3]  Alexander L. Stolyar,et al.  On the Asymptotic Optimality of the Gradient Scheduling Algorithm for Multiuser Throughput Allocation , 2005, Oper. Res..

[4]  Tara Javidi,et al.  Resource Allocation in OFDMA with Time-Varying Channel and Bursty Arrivals , 2007, IEEE Communications Letters.

[5]  Leandros Tassiulas,et al.  Linear complexity algorithms for maximum throughput in radio networks and input queued switches , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[6]  Leandros Tassiulas,et al.  Scheduling and performance limits of networks with constantly changing topology , 1997, IEEE Trans. Inf. Theory.

[7]  Frank Kelly,et al.  Charging and rate control for elastic traffic , 1997, Eur. Trans. Telecommun..

[8]  George Michailidis,et al.  ON PARALLEL QUEUING WITH RANDOM SERVER CONNECTIVITY AND ROUTING CONSTRAINTS , 2002, Probability in the Engineering and Informational Sciences.

[9]  Ioannis Lambadaris,et al.  Explicit Characterization of Stability Region for Stationary Multi-Queue Multi-Server Systems , 2011, IEEE Transactions on Automatic Control.

[10]  G. Michailidis,et al.  On the stationary dynamics of parallel queues with random server connectivities , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[11]  Leandros Tassiulas,et al.  Resource Allocation and Cross-Layer Control in Wireless Networks , 2006, Found. Trends Netw..

[12]  Lang Tong,et al.  Stability and delay of finite-user slotted ALOHA with multipacket reception , 2005, IEEE Transactions on Information Theory.

[13]  Ioannis Lambadaris,et al.  Network capacity region of multi-queue multi-server queueing system with time varying connectivities , 2010, 2010 IEEE International Symposium on Information Theory.

[14]  R. Srikant,et al.  Fair scheduling in wireless packet networks , 1999, TNET.

[15]  Ioannis Lambadaris,et al.  Optimal server assignment in multi-server parallel queueing systems with random connectivities and random service failures , 2012, 2012 IEEE International Conference on Communications (ICC).

[16]  Nitin H. Vaidya,et al.  Resource Allocation in Multi-Radio Multi-Channel Multi-Hop Wireless Networks , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[17]  Leandros Tassiulas,et al.  Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks , 1992 .

[18]  Ioannis Lambadaris,et al.  Delay optimal server assignment to symmetric parallel queues with random connectivities , 2011, IEEE Conference on Decision and Control and European Control Conference.

[19]  Leandros Tassiulas.  Scheduling and performance limits of networks with constantly changing topology , 1997 .

[20]  Ward Whitt,et al.  Comparison methods for queues and other stochastic models , 1986 .

[21]  T. Javidi.  Rate Stable Resource Allocation in OFDM Systems: From Waterfilling to Queue-Balancing , 2004 .

[22]  Ness B. Shroff,et al.  Low-Complexity Scheduling Policies for Achieving Throughput and Asymptotic Delay Optimality in Multichannel Wireless Networks , 2014, IEEE/ACM Transactions on Networking.

[23]  Leandros Tassiulas,et al.  Exploiting wireless channel State information for throughput maximization , 2004, IEEE Transactions on Information Theory.

[24]  Wei Luo,et al.  Stability of N interacting queues in random-access systems , 1999, IEEE Trans. Inf. Theory.

[25]  R. Srikant,et al.  Fair Resource Allocation in Wireless Networks Using Queue-Length-Based Scheduling and Congestion Control , 2005, IEEE/ACM Transactions on Networking.

[26]  Jean C. Walrand,et al.  Achieving 100% throughput in an input-queued switch , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[27]  Leandros Tassiulas,et al.  Dynamic server allocation to parallel queues with randomly varying connectivity , 1993, IEEE Trans. Inf. Theory.

[28]  T. Lindvall.  Lectures on the Coupling Method , 1992 .

[29]  Eytan Modiano,et al.  Optimal Transmission Scheduling in Symmetric Communication Models With Intermittent Connectivity , 2007, IEEE Transactions on Information Theory.

[30]  Leandros Tassiulas,et al.  Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks , 1990, 29th IEEE Conference on Decision and Control.

[31]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[32]  Eytan Modiano,et al.  Dynamic power allocation and routing for time-varying wireless networks , 2005 .

[33]  Ioannis Lambadaris,et al.  On the stability region of multi-queue multi-server queueing systems with stationary channel distribution , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[34]  Zhen Liu,et al.  Optimal Transmission Policies for Noisy Channels , 2001, Oper. Res..

[35]  Koushik Kar,et al.  Throughput-Optimal Scheduling in Multichannel Access Point Networks Under Infrequent Channel Measurements , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[36]  N.B. Shroff,et al.  Optimal opportunistic scheduling in wireless networks , 2003, 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall (IEEE Cat. No.03CH37484).

[37]  Jon Lee.  A First Course in Combinatorial Optimization , 2004 .

[38]  Rajeev Agrawal,et al.  Optimality of Certain Channel Aware Scheduling Policies , 2002 .

[39]  Frank Diederich,et al.  Linear And Integer Programming , 2016 .

[40]  Harold W. Kuhn,et al.  The Hungarian method for the assignment problem , 1955, 50 Years of Integer Programming.

[41]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[42]  Tara Javidi,et al.  Delay-Optimal Server Allocation in Multiqueue Multiserver Systems With Time-Varying Connectivities , 2009, IEEE Transactions on Information Theory.

[43]  Nitin H. Vaidya,et al.  Scheduling in Multi-Channel Wireless Networks , 2010, ICDCN.

[44]  Michael J. Neely,et al.  Dynamic power allocation and routing for satellite and wireless networks with time varying channels , 2003 .

[45]  N. L. Lawrie,et al.  Comparison Methods for Queues and Other Stochastic Models , 1984 .

[46]  T. Javidi,et al.  A fresh look at optimal subcarrier allocation in OFDMA systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[47]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[48]  Ioannis Lambadaris,et al.  Optimal Resource Scheduling in Wireless Multiservice Systems with Random Channel Connectivity , 2009, GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference.

[49]  Eytan Modiano,et al.  Dynamic power allocation and routing for time varying wireless networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[50]  Anthony Ephremides,et al.  Stability and Performance Issues of a Relay Assisted Multiple Access Scheme , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[51]  Ioannis Lambadaris,et al.  Throughput-optimal relay selection in multiuser cooperative relaying networks , 2010, 2010 - MILCOM 2010 MILITARY COMMUNICATIONS CONFERENCE.

[52]  R. Srikant,et al.  A tutorial on cross-layer optimization in wireless networks , 2006, IEEE Journal on Selected Areas in Communications.