Multiclass Queues under Various Service Disciplines

The author presents performance analysis of a single buffer multiple-queue system. Four different types of service disciplines (i.e., non-preemptive, pre-emptive repeat different, state dependent random polling and globally gated) are analyzed. His model includes correlated input process and three different types of non-productive time (i.e., switchover, vacation and idle time). Special cases of the model includes server with mixed multiple and single vacations, stopping server with delayed vacation and stopping server with alternating vacation and idle time. For each of the four service disciplines the key performance measures such as average customer waiting time, loss probability, and throughput are computed. The results permit a detailed discussion of how these performance measures depends on the customer arrival rate, the customer service time, the switchover time, the vacation time, and the idle time. Moreover, extensive numerical results are presented and the four service disciplines are compared with respect to the performance measure. Previous studies of the single buffer multiple-queue systems tend to provide separate analysis for the two cases of zero and nonzero switchover time. The author is able to provide a unified analysis for the two cases. His results generalize and improve a number of known results on single buffer multiple-queue systems. Furthermore, this method does not require differentiation while it is needed if one uses the probability generating function approach. Lastly, the author's approach works for all single buffer multiple-queue systems in which the next queue to be served is determines solely on the basis of the occupancy states at the end of the cycle time.

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Convex ordering of the attained waiting times in single-server queues and related problems

Journal of Applied Probability ◽

10.1017/s0021900200039802 ◽

1991 ◽

Vol 28 (02) ◽

pp. 433-445 ◽

Cited By ~ 1

Author(s):

Masakiyo Miyazawa ◽

Genji Yamazaki

Keyword(s):

Waiting Time ◽

Time Distribution ◽

Waiting Times ◽

Service Discipline ◽

Single Server ◽

Waiting Time Distribution ◽

Convex Order ◽

Convex Ordering ◽

Single Server Queues ◽

Service Disciplines

The attained waiting time of customers in service of the G/G/1 queue is compared for various work-conserving service disciplines. It is proved that the attained waiting time distribution is minimized (maximized) in convex order when the discipline is FCFS (PR-LCFS). We apply the result to characterize finiteness of moments of the attained waiting time in the GI/GI/1 queue with an arbitrary work-conserving service discipline. In this discussion, some interesting relationships are obtained for a PR-LCFS queue.

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The Service Time Properties of an Unreliable Server Characterize the Exponential Distribution

Advances in Applied Probability ◽

10.1017/s0001867800026069 ◽

1994 ◽

Vol 26 (01) ◽

pp. 172-182 ◽

Cited By ~ 1

Author(s):

Z. Khalil ◽

B. Dimitrov

Keyword(s):

Exponential Distribution ◽

Service Time ◽

Initial Conditions ◽

Mean Values ◽

Unreliable Server ◽

Service Disciplines ◽

The Mean ◽

Server Reliability ◽

Preemptive Repeat Different

Consider the total service time of a job on an unreliable server under preemptive-repeat-different and preemptive-resume service disciplines. With identical initial conditions, for both cases, we notice that the distributions of the total service time under these two disciplines coincide, when the original service time (without interruptions due to server failures) is exponential and independent of the server reliability. We show that this fact under varying server reliability is a characterization of the exponential distribution. Further we show, under the same initial conditions, that the coincidence of the mean values also leads to the same characterization.

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