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A Batch Arrival Non-Markovian Queue with Three Types of Service

by S. Maragatha Sundari, S. Srinivasan, A. Ranjitham
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 83 - Number 5
Year of Publication: 2013
Authors: S. Maragatha Sundari, S. Srinivasan, A. Ranjitham
10.5120/14448-2612

S. Maragatha Sundari, S. Srinivasan, A. Ranjitham . A Batch Arrival Non-Markovian Queue with Three Types of Service. International Journal of Computer Applications. 83, 5 ( December 2013), 43-47. DOI=10.5120/14448-2612

@article{ 10.5120/14448-2612,
author = { S. Maragatha Sundari, S. Srinivasan, A. Ranjitham },
title = { A Batch Arrival Non-Markovian Queue with Three Types of Service },
journal = { International Journal of Computer Applications },
issue_date = { December 2013 },
volume = { 83 },
number = { 5 },
month = { December },
year = { 2013 },
issn = { 0975-8887 },
pages = { 43-47 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume83/number5/14448-2612/ },
doi = { 10.5120/14448-2612 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:58:37.391645+05:30
%A S. Maragatha Sundari
%A S. Srinivasan
%A A. Ranjitham
%T A Batch Arrival Non-Markovian Queue with Three Types of Service
%J International Journal of Computer Applications
%@ 0975-8887
%V 83
%N 5
%P 43-47
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, a batch arrival non- Markovian queueing model with three types of service is considered. The customers arrive in batches of variable size. Here a single server provides three types of service ,type 1 with probability p_1, type 2 with probability p_2 and type 3 with probability p_3. The service times follows general distribution . The customer may choose either type of the services. The server follows multiple vacation. Whenever the system becomes empty, the server takes a vacation and the vacation follows general distribution. On returning from vacation if the server finds no customer waiting in the system,again the server goes for vacation. The system may breakdown at random and repair time follow exponential distribution. we assume restricted admissibility of arriving batches in which not all batches are allowed to join the system at all times. The probability generating function and some probability measures of the system are also found.

References
  1. Lee,H. W. ,Lee,S. S,. Park,J. O, and Chae,K. C. ,Analysis of the M^([x])/G/1 queue with N-policy and multiple vacations,J. Appl. Prob, 31 (1994),476-496. Chae,K. C. and Lee,H. W. , M^([x])/G/1 vacation models with N-policy: Heuristic interpretation of mean waiting time,J. Ops. Res. Soc,46 (1995),1014-1022. Arumaganathan,R. . ,Bulk queueing model with server failures and multiple vacations,Ph. D. Thesis,Bharathiyar University,Coimbatore,1997. Takagi,H. ,Queueing analysis :A founadation o
Index Terms

Computer Science
Information Sciences

Keywords

Batch arrival Probability generating function Random breakdown Restricted admissibility Multiple vacation Mean queue size.

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