IEICE TRANSACTIONS on transactions
General Model of Periodically Sampled Queues
Summary :
This paper presents a general model and analysis of periodically sampled queues, which cover a variety of real-time processing systems such as TSS computers and telecommunication switching systems. Generating functions of the number of calls in a system immediately following sampling points are formulated under the conditions of; (1) general sampling period distribution, (2) independent, identically distributed arrivals per sampling interval, (3) maximum S processing capability per sampling interval, and (4) service probability per sampling interval in accordance with the number of calls in the system immediately following sampling points. Thus, probability distributions of the number of calls at arbitrary instants are formulated as generating functions. With these, performance measures such as the average number of calls in a system and the average waiting time are derived. The universality of this model is demonstrated by special cases. Numerical examples are given to examine the effects of sampling distributions under a single server condition, taken as an example.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E68-E No.7 pp.448-455
- Publication Date
- 1985/07/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Switching Systems
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Makoto YOSHIDA, "General Model of Periodically Sampled Queues" in IEICE TRANSACTIONS on transactions,
vol. E68-E, no. 7, pp. 448-455, July 1985, doi: .
Abstract: This paper presents a general model and analysis of periodically sampled queues, which cover a variety of real-time processing systems such as TSS computers and telecommunication switching systems. Generating functions of the number of calls in a system immediately following sampling points are formulated under the conditions of; (1) general sampling period distribution, (2) independent, identically distributed arrivals per sampling interval, (3) maximum S processing capability per sampling interval, and (4) service probability per sampling interval in accordance with the number of calls in the system immediately following sampling points. Thus, probability distributions of the number of calls at arbitrary instants are formulated as generating functions. With these, performance measures such as the average number of calls in a system and the average waiting time are derived. The universality of this model is demonstrated by special cases. Numerical examples are given to examine the effects of sampling distributions under a single server condition, taken as an example.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e68-e_7_448/_p
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@ARTICLE{e68-e_7_448,
author={Makoto YOSHIDA, },
journal={IEICE TRANSACTIONS on transactions},
title={General Model of Periodically Sampled Queues},
year={1985},
volume={E68-E},
number={7},
pages={448-455},
abstract={This paper presents a general model and analysis of periodically sampled queues, which cover a variety of real-time processing systems such as TSS computers and telecommunication switching systems. Generating functions of the number of calls in a system immediately following sampling points are formulated under the conditions of; (1) general sampling period distribution, (2) independent, identically distributed arrivals per sampling interval, (3) maximum S processing capability per sampling interval, and (4) service probability per sampling interval in accordance with the number of calls in the system immediately following sampling points. Thus, probability distributions of the number of calls at arbitrary instants are formulated as generating functions. With these, performance measures such as the average number of calls in a system and the average waiting time are derived. The universality of this model is demonstrated by special cases. Numerical examples are given to examine the effects of sampling distributions under a single server condition, taken as an example.},
keywords={},
doi={},
ISSN={},
month={July},}
Copy
TY - JOUR
TI - General Model of Periodically Sampled Queues
T2 - IEICE TRANSACTIONS on transactions
SP - 448
EP - 455
AU - Makoto YOSHIDA
PY - 1985
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E68-E
IS - 7
JA - IEICE TRANSACTIONS on transactions
Y1 - July 1985
AB - This paper presents a general model and analysis of periodically sampled queues, which cover a variety of real-time processing systems such as TSS computers and telecommunication switching systems. Generating functions of the number of calls in a system immediately following sampling points are formulated under the conditions of; (1) general sampling period distribution, (2) independent, identically distributed arrivals per sampling interval, (3) maximum S processing capability per sampling interval, and (4) service probability per sampling interval in accordance with the number of calls in the system immediately following sampling points. Thus, probability distributions of the number of calls at arbitrary instants are formulated as generating functions. With these, performance measures such as the average number of calls in a system and the average waiting time are derived. The universality of this model is demonstrated by special cases. Numerical examples are given to examine the effects of sampling distributions under a single server condition, taken as an example.
ER -
English
