Busy-period analysis of a correlated queue

Borst, Sem; Combé, M.B.

doi:10.2307/3214587

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1993

2023

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Cited by 5 publications

(1 citation statement)

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“…Manageable arrival rates in queueing model have been discussed in [9][10][11] and [12][13] have expanded their research to include adjustable arrival rates in retrial queue. Busy duration perusal of correlated queues with associated incoming and outgoing procedure has been evaluated in [14]. The stability conditions and the system characteristics of mutually dependent queueing model dealt upon, as in [15].…”

Section: Introductionmentioning

confidence: 99%

Control Policy, Manageable Arrival Rates, and Reverse Balking in Mutually Dependent Queueing Model

2023

Contemp. Math.

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Section: Introductionmentioning

confidence: 99%

Control Policy, Manageable Arrival Rates, and Reverse Balking in Mutually Dependent Queueing Model

2023

Contemp. Math.

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M/M/c/K loss and delay interdependent queueing model with controllable arrival rates and no passing

Thiagarajan

Srinivasan²

2011

Sankhya B

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An M/G/1 queue with customer collection

Borst

Boxma

1993

Communications in Statistics. Stochastic Models

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This paper analyses a variant of the M / G / 1 queue in which the service times of arriving customers depend on the length of the interval between their arrival and the previous arrival. The dependence structure under consideration arises when individual customers arrive according to a Poisson process, while customer collectors are sent out according to a Poisson process to collect the customers and to bring them to the service facility. In this case collected numbers of customers, and 'hence total collected service requests, are positively correlated with the corresponding collect intervals. Viewing a batch of collected customers as one (super)customer gives rise to an M/C/1 queue with a positive cor- 342BORST, BOXMA, AND COMBE relation between service times of such customers and their interarrival times. Both for individual customers and for supercustomers we derive the transforms of the sojourn time, waiting time and queue length distributions. We also compare our results with those for the ordinary M / G / 1 queue without dependence.

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Busy-period analysis of a correlated queue

Cited by 5 publications

References 3 publications

Control Policy, Manageable Arrival Rates, and Reverse Balking in Mutually Dependent Queueing Model

Control Policy, Manageable Arrival Rates, and Reverse Balking in Mutually Dependent Queueing Model

M/M/c/K loss and delay interdependent queueing model with controllable arrival rates and no passing

An M/G/1 queue with customer collection

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