A single-server discrete-time retrial G-queue with server breakdowns and repairs

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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“…where we also use Equation (19). Since z * = 1 and under the assumption that z * = 0, the probability P(0, 0) then directly follows from (20) as…”

Section: System Contentmentioning

confidence: 99%

“…For related work on discrete-time G-queues with negative customers, the reader is referred to [3,7,14,[16][17][18][19][20][21][22][23]. For work on continuous-time queueing models with negative customers and/or disasters, we refer to the bibliography in [24,25] and the more recent papers [26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Discrete-Time Queueing Model with Disasters

2021

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“…Later on, Zhang et al [18] studied the noncooperative and cooperative strategies of customers in the context of a retrial queueing model where the server is subject to vacations, breakdowns and repairs. However, although more attention has been paid on the analysis of discrete time queueing models with unreliable server, such as Atencia and Moreno [1], Bruneel [2], Fiems et al [5][6], Moreno [9], Morozov et al [10], Vinck and Bruneel [14], Wang and Zhang [16][17], among others, it is found that there is no work concerning the equilibrium balking behavior in the discrete-time queues with server breakdowns and repairs.…”

Section: Introductionmentioning

confidence: 96%

Equilibrium Balking Strategies in the Geo/Geo/1 Queues with Server Breakdowns and Repairs

Yang

Wang

Zhao

2014

Quality Technology & Quantitative Management

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______________________________________________________________________Abstract: This paper studies the equilibrium behavior of customers in the Geo/Geo/1 queue with server breakdowns and repairs. The reliability factor is introduced into the economic analysis and customers' behavior analysis of the discrete-time queues. The server is subject to breakdowns and repairs when providing service to customers. Upon arrival, the customers decide for themselves whether to enter the system or balk based on a natural reward-cost structure and available information on hand. The behavior of customers is investigated with various levels of information regarding three states of server and the system queue length. By deriving and solving a set of system difference equations, we obtain the stationary distribution of the system and the mean sojourn time of an arriving customer. Equilibrium strategies for the customers under different levels of information are derived and the behaviors of the customers under these strategies are investigated. Finally we illustrate the effect of several parameters on the equilibrium behavior via numerical experiments.

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“…Queue with negative arrivals called G-queue was first introduced by Gelenbe [4] with a view to modeling neural networks. Wang and Zhang [9] considered a discrete time retrial queue with negative arrivals. Peng et al [7] suggested an M/G/1 retrial G-queue with pre-emptive resume priority and collisions under linear retrial policy.…”

Section: Introductionmentioning

confidence: 99%

Unreliable Batch Arrival Retrial Queue with Negative Customers, Multi-Types of Heterogeneous Service, Setup Time and Reserved Time

Kirupa¹,

Chandrika²

2015

IJCA

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Batch arrival retrial queue with positive and negative customers is considered. Server provides M types of service. Positive customers arrive in batches according to Poisson process. If the server is idle upon the arrival of a batch, one of the customers in the batch receives any one the types immediately and others join the orbit. The server is subject to two different modes of failure. Mode 1 failure occurs due to the arrival of negative customer and Mode 2 due to random breakdown of the server. In both cases, repair starts after some random amount of time. The server failed under mode 2 continues the interrupted service or waits for the same customer after the repair completion. Generating function technique is employed to obtain joint distributions of the server state and orbit length. Expected system size, expected orbit size, availability of the server and failure frequency of the server are derived. Stochastic decomposition law is also verified.

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A single-server discrete-time retrial G-queue with server breakdowns and repairs

Cited by 20 publications

References 33 publications

Analysis of a Discrete-Time Queueing Model with Disasters

Analysis of a Discrete-Time Queueing Model with Disasters

Equilibrium Balking Strategies in the Geo/Geo/1 Queues with Server Breakdowns and Repairs

Unreliable Batch Arrival Retrial Queue with Negative Customers, Multi-Types of Heterogeneous Service, Setup Time and Reserved Time

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