Waiting time distributions in a two-queue model with mixed exhaustive and gated-type K-limited services

Ozawa, Toshihisa

doi:10.1007/978-0-387-35360-9_13

Cited by 6 publications

(5 citation statements)

References 14 publications

(17 reference statements)

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“…For two-queue systems where both queues are served according to the 1-limited discipline, the problem of finding the queue length distribution can be shown to translate into a boundary value problem [6,7,11,13]. For general k, an exact evaluation for the queue-length distribution is known in two-queue exhaustive/k-limited systems (see [21,24,25,28]). The situation where both queues follow the k-limited discipline has not been solved yet.…”

Section: Introductionmentioning

confidence: 99%

HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

Boon¹,

Winands²

2014

Prob. Eng. Inf. Sci.

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In this paper, we study a two-queue polling model with zero switchover times and klimited service (serve at most k i customers during one visit period to queue i, i = 1, 2) in each queue. The arrival processes at the two queues are Poisson, and the service times are exponentially distributed. By increasing the arrival intensities until one of the queues becomes critically loaded, we derive exact heavy-traffic limits for the joint queue-length distribution using a singular-perturbation technique. It turns out that the number of customers in the stable queue has the same distribution as the number of customers in a vacation system with Erlang-k 2 distributed vacations. The queue-length distribution of the critically loaded queue, after applying an appropriate scaling, is exponentially distributed. Finally, we show that the two queue-length processes are independent in heavy traffic.

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Section: Introductionmentioning

confidence: 99%

HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

Boon¹,

Winands²

2014

Prob. Eng. Inf. Sci.

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“…Remark 3.2. For general k, an exact evaluation for the queue-length distribution is known in two-queue exhaustive/k-limited systems with zero setup times (see Lee [11] and Ozawa [15,16]) and with state-dependent switch-over times (see [28]). Remark 3.3.…”

Section: Known Results For Two-queue Polling Systemsmentioning

confidence: 99%

On open problems in polling systems

Boon¹,

Boxma²,

Winands³

2011

Queueing Syst

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In the present paper we address two open problems concerning polling systems, viz., queueing systems consisting of multiple queues attended by a single server that visits the queues one at a time. The first open problem deals with a system consisting of two queues, one of which has gated service, while the other receives 1-limited service. The second open problem concerns polling systems with general (renewal) arrivals and deterministic switch-over times that become infinitely large. We discuss related, known results for both problems, and the difficulties encountered when trying to solve them.

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“…Polling models with k-limited services also do not satisfy the branching property, making them notoriously hard to analyse; only in a few special two-queue cases an exact analysis has turned out to be feasible, see e.g. [28,29,30,31,32]. Although the polling model under investigation does not satisfy the branching property, expressions for the cycle time will be established, representing the flow time of an order.…”

Section: Polling Model Of Worktationmentioning

confidence: 99%