On the length and number of served customers of the busy period of a generalised M/G/1 queue with finite waiting room
- 1 August 1973
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 5 (02) , 379-389
- https://doi.org/10.1017/s0001867800039239
Abstract
Customers arrive in groups to a single server queue with finite waiting room. Two-dimensional distributions for times and numbers of served customers between occurrences of states in the embedded Markov chain are obtained by linear algebra giving systems of equations for joint Laplace-Stieltjes transforms. For M/M/1 a simple recursion relation for the joint transform of the two variables in the title is derived and used to obtained the first and second moments.Keywords
This publication has 3 references indexed in Scilit:
- Limit theorems for thinning of renewal point processesJournal of Applied Probability, 1972
- A model for interaction of a Poisson and a renewal process and its relation with queuing theoryJournal of Applied Probability, 1972
- On the busy periods for the M/G/1 queue with finite and with infinite waiting roomJournal of Applied Probability, 1971