Performance Evaluation Of Dependent Two-Stage Services

In many scenarios services are provided in successive stages. While tandem queues appropriately reflect the structure of such scenarios, the typical assumption that service times at different stages are independent often does not fit to reality. We examine, via simulation, the impact of dependencies among service times on expected customer waiting times. The usual network simulation overhead caused by event list handling is avoided by an extension of the Lindley recursion to the two-stage case. Numerical results are presented for exponentially and uniformly distributed service times with different types of dependencies and varying server utilizations.

[1]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[2]  T. Ikenaga,et al.  Performance analysis of queue length distribution of tandem routers for QoS measurement , 2002, Proceedings 2002 Symposium on Applications and the Internet (SAINT) Workshops.

[3]  D. V. Lindley,et al.  The theory of queues with a single server , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  Peter Buchholz,et al.  Bounding stationary results of Tandem networks with MAP input and PH service time distributions , 2006, SIGMETRICS '06/Performance '06.

[5]  Andrzej Bargiela,et al.  A model of granular data: a design problem with the Tchebyschev FCM , 2005, Soft Comput..

[6]  Ronald W. Wolff,et al.  Tandem Queues with Dependent Service Times in Light Traffic , 1982, Oper. Res..

[7]  Andrzej Bargiela,et al.  Granular prototyping in fuzzy clustering , 2004, IEEE Transactions on Fuzzy Systems.

[8]  P. Burke.  The Output of a Queuing System , 1956 .

[9]  M. R. Irving,et al.  Observability Determination in Power System State Estimation Using a Network Flow Technique , 1986, IEEE Transactions on Power Systems.

[10]  Andrzej Bargiela,et al.  Fuzzy fractal dimensions and fuzzy modeling , 2003, Inf. Sci..

[11]  K. Meyer.  The Output of a Queueing System , 1981 .

[12]  G. F. Newell.  Approximate Behavior of Tandem Queues , 1979 .

[13]  Alexander N. Dudin,et al.  The BMAP/G/1/N -> ./PH/1/M tandem queue with losses , 2005, Perform. Evaluation.

[14]  Zbigniew Palmowski,et al.  A Tandem Queue with a Gate Mechanism , 2003, Queueing Syst. Theory Appl..

[15]  Pierre L'Ecuyer,et al.  An Object-Oriented Random-Number Package with Many Long Streams and Substreams , 2002, Oper. Res..

[16]  Antonio Gómez-Corral,et al.  A Tandem Queue with Blocking and Markovian Arrival Process , 2002, Queueing Syst. Theory Appl..

[17]  R. Weber.  THE INTERCHANGEABILITY OF -/M/1 QUEUES IN SERIES , 1979 .

[18]  E. Reich.  Waiting Times When Queues are in Tandem , 1957 .

[19]  Dee Denteneer.  Models for data transmission delay in cable networks , 2006 .

[20]  Michel Mandjes.  Packet Models Revisited: Tandem and Priority Systems , 2004, Queueing Syst. Theory Appl..

[21]  Michael Pinedo,et al.  A Comparison Between Tandem Queues with Dependent and Independent Service Times , 1982, Oper. Res..