SERIE RESEARCH niEmORRnDH

Stochastic service networks are studied with inaccuracies or perturbations in the distributional forms of service and interarrival times. A condition is provided to conclude error bounds for the effect of these data imprecisions on stationary measures such as a throughput. The verification of this condition is illustrated for a Jacksonian network application with perturbed nonexponential input.

[1]  Paul Glasserman,et al.  Aggregation Approximations for Sensitivity Analysis of Multi-Class Queueing Networks , 1989, Perform. Evaluation.

[2]  David D. Yao,et al.  Stochastic Monotonicity of the Queue Lengths in Closed Queueing Networks , 1987, Oper. Res..

[3]  Ward Whitt,et al.  Stochastic Comparisons for Non-Markov Processes , 1986, Math. Oper. Res..

[4]  Rajan Suri,et al.  Infinitesimal perturbation analysis for general discrete event systems , 1987, JACM.

[5]  M. Puterman,et al.  Perturbation theory for Markov reward processes with applications to queueing systems , 1988, Advances in Applied Probability.

[6]  Xi-Ren Cao,et al.  First-Order Perturbation Analysis of a Simple Multi-Class Finite Source Queue , 1987, Perform. Evaluation.

[7]  Eugene Seneta,et al.  Finite approximations to infinite non-negative matrices , 1967, Mathematical Proceedings of the Cambridge Philosophical Society.

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

[9]  P. Schweitzer Perturbation theory and finite Markov chains , 1968 .

[10]  J. Walrand,et al.  Monotonicity of Throughput in Non-Markovian Networks. , 1989 .

[11]  N. M. van Dijk A note on extended uniformization for non-exponential stochastic networks , 1989 .

[12]  CARL D. MEYER,et al.  The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities , 1980, SIAM J. Algebraic Discret. Methods.

[13]  Henk Tijms,et al.  Stochastic modelling and analysis: a computational approach , 1986 .

[14]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

[15]  Alan S. Willsky,et al.  The reduction of perturbed Markov generators: an algorithm exposing the role of transient states , 1988, JACM.

[16]  David D. Yao,et al.  Throughput Bounds for Closed Queueing Networks with Queue-Dependent Service Rates , 1988, Perform. Evaluation.

[17]  Bernard F. Lamond,et al.  Simple Bounds for Finite Single-Server Exponential Tandem Queues , 1988, Oper. Res..

[18]  P. Whittle Partial balance and insensitivity , 1985, Journal of Applied Probability.

[19]  Xi-Ren Cao Convergence of parameter sensitivity estimates in a stochastic experiment , 1984, The 23rd IEEE Conference on Decision and Control.

[20]  Nico M. van Dijk,et al.  A Simple Throughput Bound for Large Closed Queueing Networks with Finite Capacities , 1989, Perform. Evaluation.

[21]  A. Barbour Networks of queues and the method of stages , 1976, Advances in Applied Probability.

[22]  Y. Ho,et al.  Extensions of infinitesimal perturbation analysis , 1988 .

[23]  Rajan Suri,et al.  A Concept of Monotonicity and Its Characterization for Closed Queueing Networks , 1985, Oper. Res..

[24]  W. Whitt Comparing counting processes and queues , 1981, Advances in Applied Probability.

[25]  Nico M. van Dijk,et al.  Simple Bounds for Queueing Systems with Breakdowns , 1988, Perform. Evaluation.

[26]  Nico M. van Dijk A formal proof for the insensitivity of simple bounds for finite multi-server non-exponential tandem queues based on monotonicity results , 1987 .

[27]  R. Suri,et al.  Perturbation analysis: the state of the art and research issues explained via the GI/G/1 queue , 1989, Proc. IEEE.

[28]  Christos G. Cassandras,et al.  Infinitesimal and finite perturbation analysis for queueing networks , 1982, 1982 21st IEEE Conference on Decision and Control.