Queueing systems with server vacations (server's performing non-queueing jobs) have been studied extensively since the late 70's. A considerable number of works in this area were completed in the early 80's and surveyed by Doshi in 1986. As an extension to the classical queueing system, allowing idle servers to work on non-queueing jobs makes the vacation models more applicable in a variety of systems including flexible manufacturing or service and computer communication systems. Motivated by these applications, more studies on vacation models have been done during the late 80's and 90's and surveyed in the book by Takagi in 1991 and the book by Tian and Zhang in 2006. This paper intends to provide a brief summary of the most recent research works on vacation queueing systems in the past 10 years. Keywords  server's vacation, batch arrivals, modified vacation policy, working vacations, multi-server vacation models.

http://www.orstw.org.tw/ijor/vol7no4/2-Vol.%207,%20No.4%20pp.3-8.pdf

Recent Developments in Vacation Queueing Models : A Short Survey

In recent years, achieving high energy efficiency has become one of the primary goals in manufacturing, along with maintaining high productivity and quality. In many manufacturing systems, it is sometimes possible to temporarily switch off a machine to reserve energy, and switch it back on when a certain condition is met. Indeed, production control-based shop floor continuous improvement is recognised as one of the most cost-effective ways to achieve energy-efficient production. In this paper, we study serial production lines with Bernoulli machines and finite capacity buffers and assume that some of the machines in the line can be switched on and off during the production process according to a state-based feedback control policy. Mathematical models for the system under consideration are derived and analytical methods are developed for calculating the system performance measures during transients. Specifically, exact Markovian analysis is used for two- and three-machine lines in which the switch-on/off ...

Performance analysis for serial production lines with Bernoulli Machines and Real-time WIP-based Machine switch-on/off control

Analysis of a finite-buffer bulk-service queue under Markovian arrival process with batch-size-dependent service

http://gljc.sxu.edu.cn/docs/2013-11/20131129080206440758.pdf

Equilibrium threshold strategies in observable queueing systems under single vacation policy

In this paper, application of an evolutionary strategy to positioning a GI/M/1/N-type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical experiments are presented. A cost optimization problem is solved using an evolutionary strategy for a class of queueing systems described by exponential and Erlang distributions.

http://matwbn.icm.edu.pl/ksiazki/amc/amc24/amc24414.pdf

A finite-buffer queue with a single vacation policy

Analytic and numerical aspects of batch service queues with single vacation

The finite-buffer M/G /1 queue with general bulk-service rule and single vacation

Computing queue length distributions in MAP/G/1/N queue under single and multiple vacation

This paper considers a finite-buffer batch arrival and batch service queue with single and multiple vacations. The steady-state distributions of the number of customers in the queue at service completion, vacation termination, departure, arbitrary and pre-arrival epochs have been obtained. Finally, various performance measures such as average queue length, average waiting time, probability that the server is busy, blocking probabilities, etc. are discussed along with some numerical results. The effect of certain model parameters on the key performance measures have also been investigated. The model has potential application in several areas including manufacturing, internet web-server and telecommunication systems.

On the batch arrival batch service queue with finite buffer under server's vacation: MX/GY/1/N queue

We consider a finite buffer batch service queueing system with multiple vacations wherein the input process is Markovian arrival process (MAP). The server leaves for a vacation as soon as the system empties and is allowed to take repeated (multiple) vacations. The service- and vacation- times are arbitrarily distributed. We obtain the queue length distributions at service completion, vacation termination, departure, arbitrary and pre-arrival epochs. Finally, some performance measures such as loss probability, average queue lengths are discussed. Computational procedure has been given when the service- and vacation- time distributions are of phase type (PH-distribution).

K. Sikdar

Papers

Analytic and numerical aspects of batch service queues with single vacation

The finite-buffer M/G /1 queue with general bulk-service rule and single vacation

Computing queue length distributions in MAP/G/1/N queue under single and multiple vacation

On the batch arrival batch service queue with finite buffer under server's vacation: MX/GY/1/N queue

The queue length distributions in the finite buffer bulk-service MAP/G/1 queue with multiple vacations