The Geo/Geo/1+1 Queueing System with Negative Customers

Ma, Zhanyou; Guo, Yalin; Wang, Pengcheng; Hou, Yumei

doi:10.1155/2013/182497

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…Furthermore, if customers' joining rate is the maximum probability , it is obvious that all customers enter the queue despite of different charging systems. From (8) and (15), we know the expected profits in EPP and EAP scheme models are the same.…”

Section: Analysis and Numerical Experimentsmentioning

confidence: 99%

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Pricing Analysis in Geo/Geo/1 Queueing System

Liu

2015

Mathematical Problems in Engineering

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This paper studies the equilibrium behavior of customers and optimal pricing strategies of servers in a Geo/Geo/1 queueing system. Two common pricing mechanisms are considered. The first one is called ex-post payment (EPP) scheme where the server collects tolls proportional to queue times, and the second one is called ex-ante payment (EAP) scheme where the server charges a flat fee for the total service. The server sets the toll price to maximize its own profit. It is found that, under a customer’s choice equilibrium, the two toll mechanisms are equivalent from the economic point of view. Finally, we present several numerical experiments to investigate the effects of system parameters on the equilibrium customer joining rate and servers’ profits.

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Section: Analysis and Numerical Experimentsmentioning

confidence: 99%

“…Takagi [4] focused on the performance evaluation in discrete-time systems. Subsequently, more discrete-time queueing system studies have been conducted such as [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Pricing Analysis in Geo/Geo/1 Queueing System

Liu

2015

Mathematical Problems in Engineering

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“…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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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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