A Single-Server Priority Queuing System with General Holding Times, Poisson Input, and Reverse-Order-of-Arrival Queuing Discipline

1969 ◽  
Vol 17 (2) ◽  
pp. 351-358 ◽  
Author(s):  
L. Durr
Keyword(s):  
Queuing System ◽  
Reverse Order ◽  
Single Server ◽  
Poisson Input

Availability and maintenance modeling of a batch service queuing system

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shweta Agarwal ◽  
S.B. Singh
Keyword(s):  
Distribution System ◽  
Renewal Theory ◽  
Realistic Model ◽  
Queuing System ◽  
Batch Service ◽  
Single Server ◽  
Queuing Model ◽  
Content Type ◽  
Poisson Input ◽  
Reliability Characteristics

PurposeThe purpose of the paper is to analyze reliability characteristics of batch service queuing system with a single server model that envisages Poisson input process and exponential service times under first come, first served (FCFS) queue discipline.Design/methodology/approachWith the help of renewal theory and stochastic processes, a model has been designed to discuss the reliability and its characteristics.FindingsThe instantaneous and steady-state availability along with the maintenance model of the systems subject to generalized M/Mb/1 queuing model is derived, and a few particular cases for availability are obtained as well. For supporting the developed model, a case study on electrical distribution system (EDS) has been illustrated, which also includes a comparison for the system subject to M/Mb/1 queuing model and the system without any queue (delay).Originality/valueIt is a quite realistic model that may aid to remove congestion in the system while repairing.

INFORMATION AND UNCERTAINTY IN A QUEUING SYSTEM

2007 ◽  
Vol 21 (3) ◽  
pp. 361-380 ◽  
Author(s):  
Refael Hassin
Keyword(s):  
Service Quality ◽  
Random Variables ◽  
Random Variable ◽  
Queuing System ◽  
Service Rate ◽  
Single Server ◽  
Profit Function

This article deals with the effect of information and uncertainty on profits in an unobservable single-server queuing system. We consider scenarios in which the service rate, the service quality, or the waiting conditions are random variables that are known to the server but not to the customers. We ask whether the server is motivated to reveal these parameters. We investigate the structure of the profit function and its sensitivity to the variance of the random variable. We consider and compare variations of the model according to whether the server can modify the service price after observing the realization of the random variable.

A single server Markovian queuing system with limited buffer and reverse balking

2021 ◽  
Vol 12 (7) ◽  
pp. 1774-1784
Author(s):  
Girin Saikia ◽  
Amit Choudhury
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Mutual Fund ◽  
System Size ◽  
Queuing System ◽  
Single Server ◽  
Insurance Company ◽  
Number Of Customers ◽  
Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

Some perturbation results for the single-server queue with Poisson input

1965 ◽  
Vol 2 (2) ◽  
pp. 462-466 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Service Time ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Image Position ◽  
General Service

In a previous paper [2] the author has studied the single-server queue with non-homogeneous Poisson input and general service time, with particular emphasis on the case when the parameter of the Poisson input is of the form

On queues with periodic Poisson input

1981 ◽  
Vol 18 (04) ◽  
pp. 889-900 ◽  
Author(s):  
Austin J. Lemoine
Keyword(s):  
Waiting Time ◽  
Direct Proof ◽  
Poisson Model ◽  
Fixed Time ◽  
Time Of Day ◽  
Asymptotic Distributions ◽  
Single Server ◽  
Service Time Distribution ◽  
Asymptotic Results ◽  
Poisson Input

This paper is concerned with asymptotic results for a single-server queue having periodic Poisson input and general service-time distribution, and carries forward the analysis of this model initiated in Harrison and Lemoine. First, it is shown that a theorem of Hooke relating the stationary virtual and actual waiting-time distributions for the GI/G/1 queue extends to the periodic Poisson model; it is then pointed out that Hooke's theorem leads to the extension (developed in [3]) of a related theorem of Takács. Second, it is demonstrated that the asymptotic distribution for the server-load process at a fixed ‘time of day' coincides with the distribution for the supremum, over the time horizon [0,∞), of the sum of a stationary compound Poisson process with negative drift and a continuous periodic function. Some implications of this characterization result for the computation and approximation of the asymptotic distributions are then discussed, including a direct proof, for the periodic Poisson case, of a recent result of Rolski comparing mean asymptotic customer waiting time with that of a corresponding M/G/1 system.

Virtual Waiting Time in the Single-server Queuing System with Unreliable Server

2004 ◽  
Vol 65 (12) ◽  
pp. 1968-1976 ◽  
Author(s):  
I. S. Mikadze ◽  
V. V. Khocholava ◽  
R. A. Khurodze
Keyword(s):  
Waiting Time ◽  
Queuing System ◽  
Single Server ◽  
Unreliable Server ◽  
Virtual Waiting Time
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