Analysis of a variable service speed single server queue with batch arrivals and general setup time

This paper deals with the single-server queue with batch arrivals. We show that under suitable conditions the waiting-time distribution of an individual customer has an asymptotically exponential expansion. Computationally useful characterizations of the amplitude factor and the decay parameter are given for the practically important case in which the interarrival time and the service time have phase-type distributions.

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Exponential expansion for the tail of the waiting-time probability in the single-server queue with batch arrivals

Advances in Applied Probability ◽

10.1017/s0001867800018425 ◽

1988 ◽

Vol 20 (04) ◽

pp. 880-895 ◽

Cited By ~ 3

Author(s):

J. C. W. Van Ommeren

Keyword(s):

Waiting Time ◽

Interarrival Time ◽

Single Server ◽

Waiting Time Distribution ◽

Single Server Queue ◽

Batch Arrivals ◽

Exponential Expansion ◽

Phase Type ◽

Phase Type Distributions ◽

Server Queue

This paper deals with the single-server queue with batch arrivals. We show that under suitable conditions the waiting-time distribution of an individual customer has an asymptotically exponential expansion. Computationally useful characterizations of the amplitude factor and the decay parameter are given for the practically important case in which the interarrival time and the service time have phase-type distributions.

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Batch arrival single-server queue with variable service speed and setup time

Queueing Systems ◽

10.1007/s11134-017-9533-2 ◽

2017 ◽

Vol 86 (3-4) ◽

pp. 241-260 ◽

Cited By ~ 8

Author(s):

Moeko Yajima ◽

Tuan Phung-Duc

Keyword(s):

Setup Time ◽

Batch Arrival ◽

Single Server ◽

Single Server Queue ◽

Server Queue

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The transient behaviour of a single server queue with batch arrivals

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700027981 ◽

1963 ◽

Vol 3 (2) ◽

pp. 241-248 ◽

Cited By ~ 3

Author(s):

P. J. Brockwell

Keyword(s):

Time Distribution ◽

Single Server ◽

Waiting Time Distribution ◽

Single Server Queue ◽

Fixed Size ◽

Batch Arrivals ◽

Transient Behaviour ◽

Server Queue ◽

Negative Exponential ◽

Number Of Customers

SUMMARYA queue at which arrivals occur randomly in batches of fixed size r and for which the service times are independent negative exponential variates is considered. Expressions are obtained for the moments of the transient waiting time distribution and the distribution of the number of customers in the system just before the nth batch arrives. The distribution of the number of customers served in a busy period is also determined.

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