IEICE TRANSACTIONS on transactions
Multi-Server System with Batch Arrivals of Queueing and Non-queueing Customers
Summary :
This paper presents an analysis for a multi-server system with batch arrivals of queueing and non-queueing types of customers. Customers of two types are assumed to arrive in two independent batch Poisson streams and to have exponentially distributed service times. This situation can be seen in the Facsimile Intelligent Communication System (FICS). The existing studies on the service systems which dealt with two types of customers, however, were limited to the case of Poisson arrivals. By using the generating function technique, a recursive scheme for the steady-state probabilities in the system is obtained. Traffic measures, e.g., loss probability, mean waiting time, and the probability that the number of customers in the system is zero, are deduced without any truncated error. It is shown that the above-mentioned traffic measures can be represented by only a finite set of the steady-state probabilities in spite of the infinite state space. In some special cases, it is seen that the results obtained here are consistent with the previous works. Numerical examples are shown and traffic characteristics are also discussed.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E68-E No.10 pp.691-697
- Publication Date
- 1985/10/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Switching Systems
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Yoshitaka TAKAHASHI, Tsuyoshi KATAYAMA, "Multi-Server System with Batch Arrivals of Queueing and Non-queueing Customers" in IEICE TRANSACTIONS on transactions,
vol. E68-E, no. 10, pp. 691-697, October 1985, doi: .
Abstract: This paper presents an analysis for a multi-server system with batch arrivals of queueing and non-queueing types of customers. Customers of two types are assumed to arrive in two independent batch Poisson streams and to have exponentially distributed service times. This situation can be seen in the Facsimile Intelligent Communication System (FICS). The existing studies on the service systems which dealt with two types of customers, however, were limited to the case of Poisson arrivals. By using the generating function technique, a recursive scheme for the steady-state probabilities in the system is obtained. Traffic measures, e.g., loss probability, mean waiting time, and the probability that the number of customers in the system is zero, are deduced without any truncated error. It is shown that the above-mentioned traffic measures can be represented by only a finite set of the steady-state probabilities in spite of the infinite state space. In some special cases, it is seen that the results obtained here are consistent with the previous works. Numerical examples are shown and traffic characteristics are also discussed.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e68-e_10_691/_p
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@ARTICLE{e68-e_10_691,
author={Yoshitaka TAKAHASHI, Tsuyoshi KATAYAMA, },
journal={IEICE TRANSACTIONS on transactions},
title={Multi-Server System with Batch Arrivals of Queueing and Non-queueing Customers},
year={1985},
volume={E68-E},
number={10},
pages={691-697},
abstract={This paper presents an analysis for a multi-server system with batch arrivals of queueing and non-queueing types of customers. Customers of two types are assumed to arrive in two independent batch Poisson streams and to have exponentially distributed service times. This situation can be seen in the Facsimile Intelligent Communication System (FICS). The existing studies on the service systems which dealt with two types of customers, however, were limited to the case of Poisson arrivals. By using the generating function technique, a recursive scheme for the steady-state probabilities in the system is obtained. Traffic measures, e.g., loss probability, mean waiting time, and the probability that the number of customers in the system is zero, are deduced without any truncated error. It is shown that the above-mentioned traffic measures can be represented by only a finite set of the steady-state probabilities in spite of the infinite state space. In some special cases, it is seen that the results obtained here are consistent with the previous works. Numerical examples are shown and traffic characteristics are also discussed.},
keywords={},
doi={},
ISSN={},
month={October},}
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TY - JOUR
TI - Multi-Server System with Batch Arrivals of Queueing and Non-queueing Customers
T2 - IEICE TRANSACTIONS on transactions
SP - 691
EP - 697
AU - Yoshitaka TAKAHASHI
AU - Tsuyoshi KATAYAMA
PY - 1985
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E68-E
IS - 10
JA - IEICE TRANSACTIONS on transactions
Y1 - October 1985
AB - This paper presents an analysis for a multi-server system with batch arrivals of queueing and non-queueing types of customers. Customers of two types are assumed to arrive in two independent batch Poisson streams and to have exponentially distributed service times. This situation can be seen in the Facsimile Intelligent Communication System (FICS). The existing studies on the service systems which dealt with two types of customers, however, were limited to the case of Poisson arrivals. By using the generating function technique, a recursive scheme for the steady-state probabilities in the system is obtained. Traffic measures, e.g., loss probability, mean waiting time, and the probability that the number of customers in the system is zero, are deduced without any truncated error. It is shown that the above-mentioned traffic measures can be represented by only a finite set of the steady-state probabilities in spite of the infinite state space. In some special cases, it is seen that the results obtained here are consistent with the previous works. Numerical examples are shown and traffic characteristics are also discussed.
ER -
English
