scholarly journals A Unifying Conservation Law for Single-Server Queues

2007 ◽  
Vol 44 (4) ◽  
pp. 1078-1087 ◽  
Author(s):  
Urtzi Ayesta
Keyword(s):  
Conservation Laws ◽  
Service Time ◽  
Conservation Law ◽  
Single Server ◽  
Processor Sharing ◽  
Time Sharing ◽  
Single Class ◽  
Class Time ◽  
Single Server Queues ◽  
General Service

We develop a conservation law for a multi-class GI/GI/1 queue operating under a general work-conserving scheduling discipline. For single-class single-server queues, conservation laws have been obtained for both nonanticipating and anticipating disciplines with general service time distributions. For multi-class single-server queues, conservation laws have been obtained for (i) nonanticipating disciplines with exponential service time distributions and (ii) nonpreemptive nonanticipating disciplines with general service time distributions. The unifying conservation law we develop generalizes already existing conservation laws. In addition, it covers popular nonanticipating multi-class time-sharing disciplines such as discriminatory processor sharing (DPS) and generalized processor sharing (GPS) with general service time distributions. As an application, we show that the unifying conservation law can be used to compare the expected unconditional response time under two scheduling disciplines.

scholarly journals A Unifying Conservation Law for Single-Server Queues

2007 ◽  
Vol 44 (04) ◽  
pp. 1078-1087 ◽  
Author(s):  
Urtzi Ayesta
Keyword(s):  
Conservation Laws ◽  
Service Time ◽  
Conservation Law ◽  
Single Server ◽  
Processor Sharing ◽  
Time Sharing ◽  
Single Class ◽  
Class Time ◽  
Single Server Queues ◽  
General Service

We develop a conservation law for a multi-class GI/GI/1 queue operating under a general work-conserving scheduling discipline. For single-class single-server queues, conservation laws have been obtained for both nonanticipating and anticipating disciplines with general service time distributions. For multi-class single-server queues, conservation laws have been obtained for (i) nonanticipating disciplines with exponential service time distributions and (ii) nonpreemptive nonanticipating disciplines with general service time distributions. The unifying conservation law we develop generalizes already existing conservation laws. In addition, it covers popular nonanticipating multi-class time-sharing disciplines such as discriminatory processor sharing (DPS) and generalized processor sharing (GPS) with general service time distributions. As an application, we show that the unifying conservation law can be used to compare the expected unconditional response time under two scheduling disciplines.

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.

Some perturbation results for the single-server queue with Poisson input

1965 ◽  
Vol 2 (2) ◽  
pp. 462-466 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Service Time ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Image Position ◽  
General Service

In a previous paper [2] the author has studied the single-server queue with non-homogeneous Poisson input and general service time, with particular emphasis on the case when the parameter of the Poisson input is of the form

Extremal properties of the FIFO discipline in queueing networks

1992 ◽  
Vol 29 (4) ◽  
pp. 967-978 ◽  
Author(s):  
Rhonda Righter ◽  
J. George Shanthikumar
Keyword(s):  
Likelihood Ratio ◽  
Service Time ◽  
Queueing Networks ◽  
Service Rate ◽  
Service Discipline ◽  
Single Server ◽  
Single Server Queues ◽  
First Results ◽  
Service Times ◽  
Number Of Customers

We show that using the FIFO service discipline at single server stations with ILR (increasing likelihood ratio) service time distributions in networks of monotone queues results in stochastically earlier departures throughout the network. The converse is true at stations with DLR (decreasing likelihood ratio) service time distributions. We use these results to establish the validity of the following comparisons:(i) The throughput of a closed network of FIFO single-server queues will be larger (smaller) when the service times are ILR (DLR) rather than exponential with the same means.(ii) The total stationary number of customers in an open network of FIFO single-server queues with Poisson external arrivals will be stochastically smaller (larger) when the service times are ILR (DLR) rather than exponential with the same means.We also give a surprising counterexample to show that although FIFO stochastically maximizes the number of departures by any time t from an isolated single-server queue with IHR (increasing hazard rate, which is weaker than ILR) service times, this is no longer true for networks of more than one queue. Thus the ILR assumption cannot be relaxed to IHR.Finally, we consider multiclass networks of exponential single-server queues, where the class of a customer at a particular station determines its service rate at that station, and show that serving the customer with the highest service rate (which is SEPT — shortest expected processing time first) results in stochastically earlier departures throughout the network, among all preemptive work-conserving policies. We also show that a cµ rule stochastically maximizes the number of non-defective service completions by any time t when there are random, agreeable, yields.

A conservation law for single-server queues and its applications

1991 ◽  
Vol 28 (1) ◽  
pp. 198-209 ◽  
Author(s):  
Genji Yamazaki ◽  
Hirotaka Sakasegawa ◽  
J. George Shanthikumar
Keyword(s):  
Conservation Law ◽  
Extremal Property ◽  
Service Discipline ◽  
Single Server ◽  
Processor Sharing ◽  
Equilibrium Equations ◽  
Common Mean ◽  
The Mean ◽  
Mean Queue Length ◽  
Basic Equations

We establish a conservation law for G/G/1 queues with any work-conserving service discipline using the equilibrium equations, also called the basic equations. We use this conservation law to prove an extremal property of the first-come firstserved (FCFS) service discipline: among all service disciplines that are work-conserving and independent of remaining service requirements for individual customers, the FCFS service discipline minimizes [maximizes] the mean sojourn time in a G/G/1 queue with independent (but not necessarily identical) service times with a common mean and new better [worse] than used (NBUE[NWUE]) distributions. This extends recent results of Halfin and Whitt (1990), Righter et al. (1990) and Yamazaki and Sakasegawa (1987a,b). In addition we use the conservation law to obtain an approximation for the mean queue length in a GI/GI/1 queue under the processor-sharing service discipline with finite degree of multiplicity, called LiPS discipline. Several numerical examples are presented which support the practical usefulness of the proposed approximation.

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