Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service

A retrial queueing system with two types of batch arrivals is considered. The arrivals are called type I and type II customers. The type I customers arrive in batches of size k with probability c_k and type II customers arrive in batches of size k with probability d_k. Service time distributions are identical independent distributions and are different for both type of customers. If the arriving customers are blocked due to server being busy, type I customers are queued in a priority queue of infinity capacity whereas type II customers entered into retrial group in order to seek service again after a random amount of time. For this model the joint distribution of the number of customers in the priority queue and in the retrial group in closed form is obtained. Some particular models and operating characteristics are obtained. A numerical study is also carried out.

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A queueing system with non-recurrent input and batch servicing

Journal of Applied Probability ◽

10.1017/s0021900200108757 ◽

1965 ◽

Vol 2 (02) ◽

pp. 442-448

Author(s):

C. Pearce

Keyword(s):

Distribution Function ◽

Queueing System ◽

Arrival Process ◽

Batch Service ◽

Service Times

We consider a queueing system in which arrivals occur at times , and after every kth arrival a servicing of k arrivals is begun. We assume that the number of servers is infinite. Initially, at t 0 = 0, the system is empty and the arrival process {tn } is about to start. The batch service times are independently and identically distributed with distribution function No assumption is made about the process {tn }.

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A non-exponential queueing system with independent arrivals and batch servicing

Journal of Applied Probability ◽

10.1017/s0021900200038857 ◽

1990 ◽

Vol 27 (02) ◽

pp. 401-408

Author(s):

Nico M. Van Dijk ◽

Eric Smeitink

Keyword(s):

Queue Length ◽

Queueing System ◽

Length Distribution ◽

Service Systems ◽

Batch Service ◽

Repair System ◽

Theoretical Interest ◽

Form Expression ◽

Queue Length Distribution ◽

Service Times

We study a queueing system with a finite number of input sources. Jobs are individually generated by a source but wait to be served in batches, during which the input of that source is stopped. The service speed of a server depends on the mode of other sources and thus includes interdependencies. The input and service times are allowed to be generally distributed. A classical example is a machine repair system where the machines are subject to shocks causing cumulative damage. A product-form expression is obtained for the steady state joint queue length distribution and shown to be insensitive (i.e. to depend on only mean input and service times). The result is of both practical and theoretical interest as an extension of more standard batch service systems.

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A queueing system with moving average input process and batch arrivals

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700028469 ◽

1965 ◽

Vol 5 (4) ◽

pp. 434-442 ◽

Cited By ~ 1

Author(s):

C. Pearce

Keyword(s):

Queueing System ◽

Moving Average ◽

Limiting Distribution ◽

Input Process ◽

Batch Arrivals

In a recent paper by P. D. Finch and myself [1], the solution for the limiting distribution of a moving average queueing system was obtained. In this paper the system is generalised to the case of batch arrivals in batches of size ρ > 1.

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