A cyclic service tandem queueing model with parallel queues in the first stage

Katayama, Tsuyoshi

doi:10.1080/15326348808807088

Cited by 9 publications

(17 citation statements)

References 5 publications

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“…. The only difference with the model discussed in [19] is that we introduce (deterministic) switch-over times R 2 = R 3 = 2. We assume that no time is required to switch between the two queues in the first stage, so r 1 = 0.…”

Section: Applicability Of the Modelmentioning

confidence: 99%

“…An important feature of the newly developed technique is that it can be applied to a myriad of models which lacked an analysis of the waiting-time distribution until now. One could apply the framework (possibly after some minor modifications) to obtain distributional results in all of the aforementioned special cases of the studied system [1,9,19,23,30,31,32,33,34] but also, for example, in a closed network [2], in an M/G/1 queue with permanent and transient customers [8], in a network with permanent and transient customers [3], or in a polling model with arrival rates that depend on the location of the server [4,7]. Although we study a continuous-time cyclic system with gated or exhaustive service in each queue, we may extend all results -without complicating the analysis -to discrete time, to periodic polling, to batch arrivals, or to systems with different branching-type service disciplines such as globally gated service.…”

Section: Introductionmentioning

confidence: 99%

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Waiting times in queueing networks with a single shared server

2012

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We study a queueing network with a single shared server that serves the queues in a cyclic order. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems, and robotics. Special cases of the introduced network include well-known polling models, tandem queues, systems with a waiting room, multi-stage models with parallel queues, and many others. A complicating factor of this model is that the internally rerouted customers do not arrive at the various queues according to a Poisson process, causing standard techniques to find waiting-time distributions to fail. In this paper we develop a new method to obtain exact expressions for the Laplace-Stieltjes transforms of the steady-state waiting-time distributions. This method can be applied to a wide variety of models which lacked an analysis of the waitingtime distribution until now.

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Section: Applicability Of the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Waiting times in queueing networks with a single shared server

2012

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“…. The only difference with the model discussed in [4] is that we introduce (deterministic) switch-over times r2 = r3 = 2. We assume that no time is required to switch between the two queues in the first stage, so r1 = 0.…”

Section: Approximationmentioning

confidence: 99%

Queueing networks with a single shared server

Boon

Mei

Winands³

2011

SIGMETRICS Perform. Eval. Rev.

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We study a queueing network with a single shared server, that serves the queues in a cyclic order according to the gated service discipline. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems and robotics. Special cases of the introduced network include well-known polling models and tandem queues. We derive exact limits of the mean delays under both heavy-traffic and light-traffic conditions. By interpolating between these asymptotic regimes, we develop simple closed-form approximations for the mean delays for arbitrary loads.

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“…The introduced queueing network is very general, which is illustrated by the fact that many special cases have been studied in the past. Some special case configurations are standard polling systems [33], tandem queues [20,35], multi-stage queueing models with parallel queues [15], feedback vacation queues [7,34], symmetric feedback polling systems [32,34], systems with a waiting room [1,31], and many others. Due to the intrinsic complexity of the model, previous studies on the network in its full generality were restricted to queue lengths and waiting time distributions for stable systems under the assumption of Poisson arrivals (see [6,28,29,30]).…”

Section: Introductionmentioning

confidence: 99%

Heavy traffic analysis of roving server networks

2016

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This article studies the heavy-traffic (HT) behavior of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves the system or is routed to another queue. This type of customer routing in queueing networks arises very naturally in many application areas (in production systems, computer-and communication networks, maintenance, etc.). In these networks, the single most important characteristic of the system performance is oftentimes the path time, i.e., the total time spent in the system by an arbitrary customer traversing a specific path. The current article presents the first HT asymptotic for the path-time distribution in queueing networks with a roving server under general renewal arrivals. In particular, we provide a strong conjecture for the system's behavior under HT extending the conjecture of Coffman et al. [8,9] to the roving server setting of the current article. By combining this result with novel light-traffic asymptotics, we derive an approximation of the mean path time for arbitrary values of the load and renewal arrivals. This approximation is not only highly accurate for a wide range of parameter settings, but is also exact in various limiting cases.

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A cyclic service tandem queueing model with parallel queues in the first stage

Cited by 9 publications

References 5 publications

Waiting times in queueing networks with a single shared server

Waiting times in queueing networks with a single shared server

Queueing networks with a single shared server

Heavy traffic analysis of roving server networks

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