We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Probabilistic characteristics of an M/ G/1/ m queue with two-loop hysteretic control of the service time and arrival rate.
- Authors
Zhernovyi, Yu.; Zhernovyi, K.
- Abstract
An M/ G/1/ m queueing system with the batch arrival of customers is considered. In the system, a threshold mechanism with two hysteretic loops is applied to control the service time and input flow intensity. The system receives two independent flows of customers. One of the flows is blocked in the overload mode. Operation modes are switched at the instants when the service of customers is completed. Complete blocking of the input flow starts when the queue length reaches number m. An approach based on Korolyuk's potential method is proposed for determining the probabilistic characteristics of the system. Laplace transforms of the distributions of the number of customers in the system during the busy period and of the distribution function of the busy period are found. The mean duration of the busy period is determined. Formulas are derived for the stationary distribution of the number of customers in the system, for the probability of service, and for the stationary characteristics of a queue. The results obtained are verified with the use of a simulation model developed with the help of the GPSS World tools.
- Subjects
QUEUING theory; HYSTERESIS (Economics); PROBABILISTIC generative models; LAPLACE transformation; GPSS (Computer program language)
- Publication
Journal of Communications Technology & Electronics, 2014, Vol 59, Issue 12, p1465
- ISSN
1064-2269
- Publication type
Article
- DOI
10.1134/S1064226914120171