A discrete-time single-server queueing system with an N-policy, an early setup and a generalization of the Bernoulli feedback

Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Disasters occur independently from time slot to time slot according to a Bernoulli process and result in the simultaneous removal of all customers from the queueing system. General probability distributions are allowed for both the number of customer arrivals during a slot and the length of the service time of a customer (expressed in slots). Using a two-dimensional Markovian state description of the system, we obtain expressions for the probability, generating functions, the mean values, variances and tail probabilities of both the system content and the sojourn time of an arbitrary customer under a first-come-first-served policy. The customer loss probability due to a disaster occurrence is derived as well. Some numerical illustrations are given.

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An N-policy discrete-time Geo/G/1 queue with modified multiple server vacations and Bernoulli feedback*

RAIRO - Operations Research ◽

10.1051/ro/2017027 ◽

2019 ◽

Vol 53 (2) ◽

pp. 367-387

Author(s):

Shaojun Lan ◽

Yinghui Tang

Keyword(s):

Discrete Time ◽

Queue Length ◽

Length Distribution ◽

Probability Generating Function ◽

Renewal Theory ◽

Function Technique ◽

Single Server ◽

Bernoulli Feedback ◽

Queue Length Distribution ◽

Special Cases

This paper deals with a single-server discrete-time Geo/G/1 queueing model with Bernoulli feedback and N-policy where the server leaves for modified multiple vacations once the system becomes empty. Applying the law of probability decomposition, the renewal theory and the probability generating function technique, we explicitly derive the transient queue length distribution as well as the recursive expressions of the steady-state queue length distribution. Especially, some corresponding results under special cases are directly obtained. Furthermore, some numerical results are provided for illustrative purposes. Finally, a cost optimization problem is numerically analyzed under a given cost structure.

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On the discrete-time Geo/G/1 retrial queueing system with preemptive resume and Bernoulli feedback

OPSEARCH ◽

10.1007/s12597-015-0218-5 ◽

2015 ◽

Vol 53 (1) ◽

pp. 116-130 ◽

Cited By ~ 1

Author(s):

Yi Peng

Keyword(s):

Discrete Time ◽

Queueing System ◽

Bernoulli Feedback ◽

Retrial Queueing System ◽

Preemptive Resume ◽

Retrial Queueing

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Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy

Operations Research and Decisions ◽

10.37190/ord200401 ◽

2020 ◽

Vol 30 (4) ◽

Author(s):

Amina Angelika Bouchentouf ◽

Lahcene Yahiaoui ◽

Mokhtar Kadi ◽

Shakir Majid

Keyword(s):

Queueing System ◽

Cost Model ◽

Probability Generating Function ◽

Steady State Solution ◽

Stochastic Decomposition ◽

Single Server ◽

Working Vacation ◽

Bernoulli Feedback ◽

Markovian Queue ◽

Retention Of Reneged Customers

This paper deals with customers’ impatience behaviour for single server Markovian queueing system under K-variant working vacation policy, waiting server, Bernoulli feedback, balking, reneging, and retention of reneged customers. Using probability generating function (PGF) technique, we obtain the steady-state solution of the system. In addition, we prove the stochastic decomposition properties. Useful performance measures of the considered queueing system are derived. A cost model is developed. Then, the parameter optimisation is carried out numerically, using quadratic fit search method (QFSM). Finally, numerical examples are provided in order to visualize the analytical results.

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