Analysis of the M/G/1 queue with discriminatory random order service policy

Kim, Jeongsim; Kim, Jerim; Kim, Bara

doi:10.1016/j.peva.2010.12.001

Cited by 14 publications

(24 citation statements)

References 15 publications

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“…However, since the service discipline is non-preemptive, non-anticipating and all class-k customers in the queue are stochastically equivalent, the distribution of the queue-length vector does not depend on the particular choice of the intraclass policy. Hence, for any arbitrary work-conserving intra-class policy we have the following result from [14]. …”

Section: Queue Length At Departure Epochsmentioning

confidence: 99%

“…Before focusing on the heavy-traffic regime, we will introduce a system of equations that is satisfied by the probability generating function of the queue-length distribution at departure epochs, as obtained by Kim, Kim, and Kim [14]. Define…”

Section: Queue Length At Departure Epochsmentioning

confidence: 99%

“…In [14], the distribution of the queue length was studied assuming that the intra-class scheduling is uniform random. However, since the service discipline is non-preemptive, non-anticipating and all class-k customers in the queue are stochastically equivalent, the distribution of the queue-length vector does not depend on the particular choice of the intraclass policy.…”

Section: Queue Length At Departure Epochsmentioning

confidence: 99%

“…For the random intra-class scheduling discipline, we have from [14] the following result for the transform T l (u, z).…”

Section: Waiting Timementioning

confidence: 99%

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Heavy-Traffic Analysis of a Non-Preemptive Multi-Class Queue With Relative Priorities

Izagirre

Verloop

Ayesta

2015

Prob. Eng. Inf. Sci.

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We study the steady-state queue-length vector in a multi-class queue with relative priorities. Upon service completion, the probability that the next served customer is from class k is controlled by class-dependent weights. Once a customer has started service, it is served without interruption until completion. We establish a state-space collapse for the scaled queue-length vector in the heavy-traffic regime, that is, in the limit the scaled queue-length vector is distributed as the product of an exponentially distributed random variable and a deterministic vector. We observe that the scaled queue length reduces as classes with smaller mean service requirement obtain relatively larger weights. We finally show that the scaled waiting time of a class-k customer is distributed as the product of two exponentially distributed random variables.

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Section: Queue Length At Departure Epochsmentioning

confidence: 99%

Section: Queue Length At Departure Epochsmentioning

confidence: 99%

Section: Queue Length At Departure Epochsmentioning

confidence: 99%

“…For the random intra-class scheduling discipline, we have from [14] the following result for the transform T l (u, z).…”

Section: Waiting Timementioning

confidence: 99%

See 2 more Smart Citations

Heavy-Traffic Analysis of a Non-Preemptive Multi-Class Queue With Relative Priorities

Izagirre

Verloop

Ayesta

2015

Prob. Eng. Inf. Sci.

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“…We mention, among others, priority scheduling (see, e.g., [4,8,11,13,15]), weighted fair queueing (WFQ) (see, e.g., [14,17]), random order of service (ROS) (see, e.g., [1,3,10]), and generalized processor sharing (GPS) (see, e.g., [9,12,16]). Strangely enough, only few results have been derived for multi-class First-Come-First-Served (FCFS) systems, i.e., queueing systems in which the customers of different classes are accommodated in one queue and served in their order of arrival, irrespective of the classes they belong to (a recent paper is [5]).…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Two-Class FCFS Queueing System with Interclass Correlation

Bruneel

Maertens

Steyaert

et al. 2012

Analytical and Stochastic Modeling Techniques and Applications

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Abstract. This paper considers a discrete-time queueing system with one server and two classes of customers. All arriving customers are accommodated in one queue, and are served in a First-Come-First-Served order, regardless of their classes. The total numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. The classes of consecutively arriving customers, however, are correlated in a Markovian way, i.e., the probability that a customer belongs to a class depends on the class of the previously arrived customer. Service-time distributions are assumed to be general but class-dependent. We use probability generating functions to study the system analytically. The major aim of the paper is to estimate the impact of the interclass correlation in the arrival stream on the queueing performance of the system, in terms of the (average) number of customers in the system and the (average) customer delay and customer waiting time.

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Stability Criterion of a General Multiserver Multiclass Queueing System

Morozov

2014

Information Sciences and Systems 2014

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Analysis of the M/G/1 queue with discriminatory random order service policy

Cited by 14 publications

References 15 publications

Heavy-Traffic Analysis of a Non-Preemptive Multi-Class Queue With Relative Priorities

Heavy-Traffic Analysis of a Non-Preemptive Multi-Class Queue With Relative Priorities

Analysis of a Two-Class FCFS Queueing System with Interclass Correlation

Stability Criterion of a General Multiserver Multiclass Queueing System

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