论文信息 - ON A SINGLE-SERVER QUEUE WITH GROUP ARRIVALS

ON A SINGLE-SERVER QUEUE WITH GROUP ARRIVALS

The queueing system GIIG/1 with group arrivals and individual service of the customers is considered. For the stable situation the limiting distribution of the waiting time distribution of the k th served customer for k -- 0c is derived by using the theory of regenerative processes. It is assumed that the group sizes are i.i.d. variables of which the distribution is aperiodic. The relation between this limiting distribution and the stationary distribution of the virtual waiting time is derived.

J. W. Cohen

[1] P. J. Burke. Technical Note - Delays in Single-Server Queues with Batch Input , 1975, Oper. Res..

[2] Vincent Hodgson,et al. The Single Server Queue. , 1972 .

[3] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1967 .

[4] Jacob Cohen,et al. On regenerative processes in queueing theory , 1976 .

[5] S. Stidham. Regenerative processes in the theory of queues, with applications to the alternating-priority queue , 1972, Advances in Applied Probability.

[6] W. Feller,et al. An Introduction to Probability Theory and Its Applications, Vol. II , 1972, The Mathematical Gazette.