A Multiserver Tandem Queue with a Specialist Server Operating with a Vacation Strategy

2020 ◽  
Vol 81 (4) ◽  
pp. 760-773
Author(s):  
T. S. Sinu Lal ◽  
A. Krishnamoorthy ◽  
V. C. Joshua
Keyword(s):  
Tandem Queue

A. B. Clarke's Tandem Queue Revisited—Sojourn Times

2008 ◽  
Vol 26 (6) ◽  
pp. 1111-1135 ◽  
Author(s):  
A. Gómez-Corral ◽  
M.E. Martos
Keyword(s):  
Tandem Queue ◽  
Sojourn Times

Regeneration in tandem queues with multiserver stations

1988 ◽  
Vol 25 (02) ◽  
pp. 391-403 ◽  
Author(s):  
Karl Sigman
Keyword(s):  
Markov Chain ◽  
Renewal Process ◽  
Single Server ◽  
Tandem Queues ◽  
Random Assignment ◽  
Tandem Queue ◽  
Ergodic Markov Chain ◽  
Fifo Queue ◽  
Harris Chain ◽  
Server System

A tandem queue with a FIFO multiserver system at each stage, i.i.d. service times and a renewal process of external arrivals is shown to be regenerative by modeling it as a Harris-ergodic Markov chain. In addition, some explicit regeneration points are found. This generalizes the results of Nummelin (1981) in which a single server system is at each stage and the result of Charlot et al. (1978) in which the FIFO GI/GI/c queue is modeled as a Harris chain. In preparing for our result, we study the random assignment queue and use it to give a new proof of Harris ergodicity of the FIFO queue.

scholarly journals PERFORMANCE MEASURES FOR THE TWO-NODE QUEUE WITH FINITE BUFFERS

2019 ◽  
Vol 34 (4) ◽  
pp. 522-549
Author(s):  
Yanting Chen ◽  
Xinwei Bai ◽  
Richard J. Boucherie ◽  
Jasper Goseling
Keyword(s):  
Random Walk ◽  
Performance Measures ◽  
Approximation Scheme ◽  
Queueing System ◽  
Original Model ◽  
Finite Capacity ◽  
Tandem Queue ◽  
Finite Buffers ◽  
Perturbed Random Walk ◽  
Markov Reward

We consider a two-node queue modeled as a two-dimensional random walk. In particular, we consider the case that one or both queues have finite buffers. We develop an approximation scheme based on the Markov reward approach to error bounds in order to bound performance measures of such random walks. The approximation scheme is developed in terms of a perturbed random walk in which the transitions along the boundaries are different from those in the original model and the invariant measure of the perturbed random walk is of product-form. We then apply this approximation scheme to a tandem queue and some variants of this model, for the case that both buffers are finite. The modified approximation scheme and the corresponding applications for a two-node queueing system in which only one of the buffers has finite capacity have also been discussed.

Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

1999 ◽  
Vol 31 (04) ◽  
pp. 1095-1117 ◽  
Author(s):  
Hyun-Soo Ahn ◽  
Izak Duenyas ◽  
Rachel Q. Zhang
Keyword(s):  
Numerical Study ◽  
Stochastic Scheduling ◽  
Static Case ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Cross Training ◽  
Dynamic Case ◽  
Sufficient And Necessary Conditions

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

A single server tandem queue

1971 ◽  
Vol 8 (1) ◽  
pp. 95-109 ◽  
Author(s):  
Sreekantan S. Nair
Keyword(s):  
Waiting Time ◽  
Queue Length ◽  
Busy Period ◽  
Single Server ◽  
Queueing Model ◽  
Tandem Queue ◽  
Limiting Behavior ◽  
Virtual Waiting Time ◽  
Priority Model

Avi-Itzhak, Maxwell and Miller (1965) studied a queueing model with a single server serving two service units with alternating priority. Their model explored the possibility of having the alternating priority model treated in this paper with a single server serving alternately between two service units in tandem.Here we study the distribution of busy period, virtual waiting time and queue length and their limiting behavior.

Transient Behaviour of a Tandem Queue

1967 ◽  
Vol 13 (9) ◽  
pp. 631-639 ◽  
Author(s):  
N. U. Prabhu
Keyword(s):  
Tandem Queue ◽  
Transient Behaviour

A conservation property for general GI/G/1 queues with an application to tandem queues

1979 ◽  
Vol 11 (03) ◽  
pp. 660-672 ◽  
Author(s):  
E. Nummelin
Keyword(s):  
Limit Theorem ◽  
Total Variation ◽  
Renewal Process ◽  
Markov Renewal Process ◽  
Output Process ◽  
Tandem Queues ◽  
Tandem Queue ◽  
Input Process ◽  
Conservation Property ◽  
Positive Recurrent

We show that, if the input process of a generalGI/G/1 queue is a positive recurrent Markov renewal process then the output process, too, is a positive recurrent Markov renewal process (the conservation property). As an application we consider a general tandem queue and prove a total variation limit theorem for the associated waiting and service times.

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