Perturbation analysis of closed queueing networks with general service time distributions

1991 ◽  
Vol 36 (11) ◽  
pp. 1327-1331
Author(s):  
X.-R. Cao
Keyword(s):  
Perturbation Analysis ◽  
Service Time ◽  
Queueing Networks ◽  
Closed Queueing Networks ◽  
General Service

Notes on the stability of closed queueing networks

1989 ◽  
Vol 26 (3) ◽  
pp. 678-682 ◽  
Author(s):  
Karl Sigman
Keyword(s):  
Service Time ◽  
Continuous Time ◽  
Queueing Networks ◽  
Queue Length ◽  
Sufficient Conditions ◽  
Time Process ◽  
Closed Queueing Networks ◽  
The Stability ◽  
General Service ◽  
Residual Service

A new proof of the stability of closed Jackson-type queueing networks (with general service-time distributions) is given and sufficient conditions are given for obtaining Cesaro, weak and total variation convergence of the continuous-time joint queue length and residual service-time process to a limiting distribution. The result weakens the sufficient conditions (for stability) of Borovkov (1986) by allowing more general service-time distributions.

Notes on the stability of closed queueing networks

1989 ◽  
Vol 26 (03) ◽  
pp. 678-682 ◽  
Author(s):  
Karl Sigman
Keyword(s):  
Service Time ◽  
Continuous Time ◽  
Queueing Networks ◽  
Queue Length ◽  
Sufficient Conditions ◽  
Time Process ◽  
Closed Queueing Networks ◽  
The Stability ◽  
General Service ◽  
Residual Service

A new proof of the stability of closed Jackson-type queueing networks (with general service-time distributions) is given and sufficient conditions are given for obtaining Cesaro, weak and total variation convergence of the continuous-time joint queue length and residual service-time process to a limiting distribution. The result weakens the sufficient conditions (for stability) of Borovkov (1986) by allowing more general service-time distributions.

Calculation of sensitivities of throughputs and realization probabilities in closed queueing networks with finite buffer capacities

1989 ◽  
Vol 21 (1) ◽  
pp. 181-206 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Perturbation Analysis ◽  
Queueing Networks ◽  
Queueing Network ◽  
Theoretical Background ◽  
System Throughput ◽  
Single Server ◽  
Finite Buffer ◽  
Closed Queueing Networks ◽  
Steady State Probability ◽  
Single Class

Perturbation analysis is an efficient approach to estimating the sensitivities of the performance measures of a queueing network. A new notion, called the realization probability, provides an alternative way of calculating the sensitivity of the system throughput with respect to mean service times in closed Jackson networks with single class customers and single server nodes (Cao (1987a)). This paper extends the above results to systems with finite buffer sizes. It is proved that in an indecomposable network with finite buffer sizes a perturbation will, with probability 1, be realized or lost. For systems in which no server can directly block more than one server simultaneously, the elasticity of the expected throughput can be expressed in terms of the steady state probability and the realization probability in a simple manner. The elasticity of the throughput when each customer’s service time changes by the same amount can also be calculated. These results provide some theoretical background for perturbation analysis and clarify some important issues in this area.

Smoothed Perturbation Analysis for Single-Server Queues by Some General Service Disciplines

1997 ◽  
Vol 29 (2) ◽  
pp. 545-566 ◽  
Author(s):  
Naoto Miyoshi ◽  
Toshiharu Hasegawa
Keyword(s):  
Perturbation Analysis ◽  
Service Time ◽  
Single Server ◽  
Single Server Queues ◽  
The Family ◽  
Service Disciplines ◽  
Preemptive Resume Priority ◽  
Queueing Processes ◽  
Strongly Consistent ◽  
General Service

We consider some single-server queues with general service disciplines, where the family of the queueing processes are parameterized by the service time distributions. Through the smoothed perturbation analysis (SPA) technique, we present under some mild conditions a unified approach to give the strongly consistent estimator for the gradient of the steady-state mean sojourn time with respect to the parameter of service time distributions, provided that it exists. Although the implementation of the SPA requires the additional sub-paths in general, the derived estimator is given as suitable for single-run computation. Simulation results are presented for queues with non-preemptive and preemptive-resume priority disciplines which demonstrate the performance of our estimators.

Smoothed Perturbation Analysis for Single-Server Queues by Some General Service Disciplines

1997 ◽  
Vol 29 (02) ◽  
pp. 545-566
Author(s):  
Naoto Miyoshi ◽  
Toshiharu Hasegawa
Keyword(s):  
Perturbation Analysis ◽  
Service Time ◽  
Single Server ◽  
Single Server Queues ◽  
The Family ◽  
Service Disciplines ◽  
Preemptive Resume Priority ◽  
Queueing Processes ◽  
Strongly Consistent ◽  
General Service

We consider some single-server queues with general service disciplines, where the family of the queueing processes are parameterized by the service time distributions. Through the smoothed perturbation analysis (SPA) technique, we present under some mild conditions a unified approach to give the strongly consistent estimator for the gradient of the steady-state mean sojourn time with respect to the parameter of service time distributions, provided that it exists. Although the implementation of the SPA requires the additional sub-paths in general, the derived estimator is given as suitable for single-run computation. Simulation results are presented for queues with non-preemptive and preemptive-resume priority disciplines which demonstrate the performance of our estimators.

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