Analysis of the asymmetric shortest queue problem with threshold jockeying

Adan, Ijbf Ivo; Wessels, J Jaap; Zijm, Willem H.M.

doi:10.1080/15326349108807209

Cited by 79 publications

(68 citation statements)

References 15 publications

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“…Our results agree with the ones obtained by Adan et al (1991). Our proof could be potentially used to generalize the above expressions to the GI/(M/1) c model with r difference jockeying.…”

Section: Examplesupporting

confidence: 82%

“…Since Haight (1958) proposed and solved the shorter queue model (the shortest queue model with only two servers), the jockeying problem has been studied extensively, in particular by Disney and Mitchell (1971), Elsayed and Bastani (1985), Kao and Lin (1990), Zhao and Grassmann (1990), Zhao (1990), and Adan, Wessels and Zijm (1991). Except Zhao and Grassmann, all authors considered only models with Markovian inputs.…”

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confidence: 99%

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Queueing Analysis of a Jockeying Model

Zhao

Grassmann

1995

Operations Research

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In this paper, we solve a type of shortest queue problem, which is related to multibeam satellite systems. We assume that the packet interarrival times are independently distributed according to an arbitrary distribution function, that the service times are Markovian with possibly different service rates, that each server has its own buffer for packet waiting, and that jockeying among buffers is permitted. Packets always join the shortest buffer(s). Jockeying takes place as soon as the difference between the longest and shortest buffers exceeds a preset number (not necessarily 1). In this case, the last packet in a longest buffer jockeys instantaneously to the shortest buffer(s). We prove that the equilibrium distribution of packets in the system is modified vector geometric. Expressions of main performance measures, including the average number of packets in the system, the average packet waiting time in the system, and the average number of jockeying, are given. Based on these solutions, numerical results are computed. By comparing the results for jockeying and nonjockeying models, we show that a significant improvement of the system performance is achieved for the jockeying model.

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“…Our results agree with the ones obtained by Adan et al (1991). Our proof could be potentially used to generalize the above expressions to the GI/(M/1) c model with r difference jockeying.…”

Section: Examplesupporting

confidence: 82%

mentioning

confidence: 99%

Queueing Analysis of a Jockeying Model

Zhao

Grassmann

1995

Operations Research

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“…There exists an extensive literature on dispatching policies and their optimality [9,26,27,35,36,37,42,46]. Among the dispatching policies, the join-the-shortest-queue (JSQ) policy has received considerable attention [5,6,10,19,20,23,24,28,30,44,45]. The JSQ policy in some scenarios has been proven to be the optimal policy; on the one hand it minimizes the customers mean waiting time [25] and on the other hand it stochastically maximizes the number of customers served by time t, t > 0 [43].…”

Section: Introductionmentioning

confidence: 99%

The shorter queue polling model

et al. 2013

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We consider a two-queue polling model in which customers upon arrival join the shorter of two queues. Customers arrive according to a Poisson process and the service times in both queues are independent and identically distributed random variables having the exponential distribution. The two-dimensional process of the numbers of customers at the queue where the server is and at the other queue is a two-dimensional Markov process. We derive its equilibrium distribution using two methodologies: the compensation approach and a reduction to a boundary value problem.

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“…In the present case we could only prove absolute convergence on the set A, which was determined by N. If N = r, then A represents the whole first quadrant of the grid, but for N > r, there are also states for which xm,n(OO) was formally defined, but may not converge absolutely. A similar feature was already encountered in the case of the asymmetic shortest queue problem (d. [2]) and also in the case of general random walks on the first quadrant with transitions to neighbours only (d. [4]). The remaining question is of course: how large can N be?…”

Section: Conclusion and Commentsmentioning

confidence: 70%

“…a job jumps to the other queue as soon as this would improve its perspectives). In [2] it has been shown that the equilibrium probabilities Pm,n of the instantaneous jockeying problem can be expressed as…”

Section: The Quest For Feasible Ao'smentioning

confidence: 99%

Shortest expected delay routing for Erlang servers

Adan

Wessels

1996

Queueing Syst

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The queueing problem with a Poisson arrival stream and two identical Erlang servers is analysed for the queueing discipline based on shortest expected delay. This queueing problem may be represented as a random walk on the integer grid in the first quadrant of the plane. In the paper it is shown that the equilibrium distribution of this random walk can be written as a countable linear combination of product forms. This linear combination is constructed in a compensation procedure. In this case the compensation procedure is essentially more complicated than in other cases where the same idea was exploited. The reason for the complications is that in this case the boundary consists of several layers which in turn is caused by the fact that transitions starting in inner states are not restricted to end in neighbouring states.Good starting solutions for the compensation procedure are found by solving the shortest expected delay problem with the same service distributions but with instantaneous jockeying.It is also shown that the results can be used for an efficient computation of relevant performance criteria.

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Analysis of the asymmetric shortest queue problem with threshold jockeying

Cited by 79 publications

References 15 publications

Queueing Analysis of a Jockeying Model

Queueing Analysis of a Jockeying Model

The shorter queue polling model

Shortest expected delay routing for Erlang servers

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