Statistical Analysis of Generalized Processor Sharing Scheduling Discipline

We develop bounds on the individual session backlog and delay distribution under the generalized processor sharing (GPS) scheduling discipline. This work is motivated by, and is an extension of, Parekh and Gallager's (see IEEE/ACM Trans. Networking, vol.1, no.6, p.344-357, 1993, and vol. 2, no.4, p.137-150, 1994) deterministic study of the GPS scheduling discipline with leaky-bucket token controlled sessions. Using the exponentially bounded burstiness (EBB) process model introduced by Yaron and Sidi (see IEEE/ACM Trans. Networking, vol.1, p.372-385, 1993) as a source traffic characterization, we establish results that extend the deterministic study of GPS. For a single GPS server in isolation, we present statistical bounds on the distributions of backlog and delay for each session. In the network setting, we show that networks belonging to a broad class of GPS assignments, the so-called consistent relative session treatment (CRST) GPS assignments, are stable in a stochastic sense. In particular, we establish simple bounds on the distribution of backlog and delay for each session in a rate proportional processor sharing (RPPS) GPS network with arbitrary topology. >

[1]  Hamid Ahmadi,et al.  Equivalent Capacity and Its Application to Bandwidth Allocation in High-Speed Networks , 1991, IEEE J. Sel. Areas Commun..

[2]  Jean C. Walrand,et al.  Effective bandwidths for multiclass Markov fluids and other ATM sources , 1993, TNET.

[3]  S. J. Golestani.  A stop-and-go queueing framework for congestion management , 1990, SIGCOMM 1990.

[4]  David Clark,et al.  Supporting Real-Time Applications in an Integrated Services Packet Network: Architecture and Mechanism , 1992, SIGCOMM.

[5]  Donald F. Towsley,et al.  Call admission control schemes under generalized processor sharing scheduling , 1997, Telecommun. Syst..

[6]  Rene L. Cruz,et al.  A calculus for network delay, Part I: Network elements in isolation , 1991, IEEE Trans. Inf. Theory.

[7]  Domenico Ferrari,et al.  Rate-controlled static-priority queueing , 1993, IEEE INFOCOM '93 The Conference on Computer Communications, Proceedings.

[8]  Moshe Sidi,et al.  Generalized processor sharing networks with exponentially bounded burstiness arrivals , 1994, Proceedings of INFOCOM '94 Conference on Computer Communications.

[9]  Debasis Mitra,et al.  Effective bandwidth of general Markovian traffic sources and admission control of high speed networks , 1993, TNET.

[10]  Moshe Sidi,et al.  Performance and stability of communication networks via robust exponential bounds , 1993, TNET.

[11]  Don Towsley,et al.  Exponential bounds for a class of stochastic processes with application to call admission control in networks , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[12]  S. Jamaloddin Golestani.  Duration-limited statistical multiplexing of delay-sensitive traffic in packet networks , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.

[13]  Srinivasan Keshav,et al.  Rate controlled servers for very high-speed networks , 1990, [Proceedings] GLOBECOM '90: IEEE Global Telecommunications Conference and Exhibition.

[14]  Cheng-Shang Chang,et al.  Stability, queue length, and delay of deterministic and stochastic queueing networks , 1994, IEEE Trans. Autom. Control..

[15]  Scott Shenker,et al.  Analysis and simulation of a fair queueing algorithm , 1989, SIGCOMM 1989.

[16]  Rene L. Cruz,et al.  A calculus for network delay, Part II: Network analysis , 1991, IEEE Trans. Inf. Theory.

[17]  James F. Kurose,et al.  On computing per-session performance bounds in high-speed multi-hop computer networks , 1992, SIGMETRICS '92/PERFORMANCE '92.

[18]  Abhay Parekh,et al.  A generalized processor sharing approach to flow control in integrated services networks: the single-node case , 1993, TNET.

[19]  Jim Kurose,et al.  On per-session end-to-end delay and the call admission problem for real-time applications with QOS r , 1994 .

[20]  N. Duffield,et al.  Exponential upper bounds via martingales for multiplexers with Markovian arrivals , 1994 .