Waiting-Time Approximations for Multiple-Server Polling Systems

We consider multiple-server polling systems, in which each of the servers visits the queues according to its own cyclic schedule. Such systems appear to completely defy the derivation of exact waiting-time results, which motivates the search for accurate approximations. In the present paper, we derive waiting-time approximations for asymmetric systems with the exhaustive and gated service discipline. The approximations are tested for a wide range of parameter combinations.

[1]  W. P. Groenendijk.  WAITING-TIME APPROXIMATIONS FOR CYCLIC-SERVICE SYSTEMS WITH MIXED SERVICE STRATEGIES , 1988 .

[2]  Onno J. Boxma,et al.  Workloads and waiting times in single-server systems with multiple customer classes , 1989, Queueing Syst. Theory Appl..

[3]  Hideaki Takagi,et al.  Application of Polling Models to Computer Networks , 1991, Comput. Networks ISDN Syst..

[4]  Uri Yechiali,et al.  AnM/M/s Queue with Servers''Vacations , 1976 .

[5]  Laxmi N. Bhuyan,et al.  Approximate Analysis of Single and Multiple Ring Networks , 1989, IEEE Trans. Computers.

[6]  Sid Browne,et al.  Parallel Service with Vacations , 1995, Oper. Res..

[7]  R. D. van der Mei,et al.  Analysis of multiple-server polling systems by means of the power-series algorithm , 1994 .

[8]  V. Schmidt,et al.  Queues and Point Processes , 1983 .

[9]  Marco Ajmone Marsan,et al.  Cycles and waiting times in symmetric exhaustive and gated multiserver multiqueue systems , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[10]  Edward P. C. Kao,et al.  Analyses of an M/M/N/ queue with server's vacations , 1991 .

[11]  V. C. Hamacher,et al.  Approximate Analysis of Non-Exhautive Multiserver Polling Systems with Applications to Local Area Networks , 1989, Comput. Networks.

[12]  Marco Ajmone Marsan,et al.  Multiserver multiqueue systems with limited service and zero walk time , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.

[13]  Onno Boxma,et al.  Pseudo-conservation laws in cyclic-service systems , 1986 .

[14]  Wayne M. Loucks,et al.  Short-Packet Transfer Performance in Local Area Ring Networks , 1985, IEEE Transactions on Computers.

[15]  Marcel F. Neuts,et al.  A Markovian Queue with N Servers Subject to Breakdowns and Repairs , 1979 .

[16]  Gideon Weiss,et al.  Dynamic priority rules when polling with multiple parallel servers , 1992, Oper. Res. Lett..

[17]  Boudewijn R. Haverkort.  Performance of computer communication systems , 1998 .

[18]  Marco Ajmone Marsan,et al.  Analysis of symmetric nonexhaustive polling with multiple servers , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.

[19]  Hideaki Takagi,et al.  Stochastic Analysis of Computer and Communication Systems , 1990 .

[20]  R. D. van der Mei,et al.  Expected delay analysis of polling systems in heavy traffic , 1998, Advances in Applied Probability.

[21]  Hong Linh Truong,et al.  Mean-delay approximation for cyclic-service queueing systems , 1983, Perform. Evaluation.

[22]  Jon G. Kuhl,et al.  An Integrated Approach to Distributed Demand Assignment in Multiple-Bus Local Networks , 1989, IEEE Trans. Computers.

[23]  Sem C. Borst,et al.  Polling systems with multiple coupled servers , 1995, Queueing Syst. Theory Appl..

[24]  Paul E. Wright,et al.  GATED, EXHAUSTIVE, PARALLEL SERVICE , 1992 .

[25]  S. Brumelle.  On the relation between customer and time averages in queues , 1971 .

[26]  Marco Ajmone Marsan,et al.  GSPN Models of Markovian Multiserver Multiqueue Systems , 1990, Perform. Evaluation.

[27]  David Everitt.  Simple Approximations for Token Rings , 1986, IEEE Trans. Commun..