1965
DOI: 10.1137/1110066
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Existence of a Limit Distribution in Queueing Systems with Bounded Sojourn Time

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1967
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Cited by 12 publications
(8 citation statements)
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“…The papers listed above all consider diffusion control problems that admit pathwise solutions. 1 Because the solution of the diffusion control problem is nontrivial in our case, we must solve it by explicitly constructing a solution to the associated Hamilton-Jacobi-Bellman (HJB) equations using the approach in Kumar and Muthuraman [24]. We then verify that the solution to the HJB equations is indeed the optimal value function for the diffusion control problem.…”
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confidence: 99%
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“…The papers listed above all consider diffusion control problems that admit pathwise solutions. 1 Because the solution of the diffusion control problem is nontrivial in our case, we must solve it by explicitly constructing a solution to the associated Hamilton-Jacobi-Bellman (HJB) equations using the approach in Kumar and Muthuraman [24]. We then verify that the solution to the HJB equations is indeed the optimal value function for the diffusion control problem.…”
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confidence: 99%
“…A natural way to incorporate impatience is to assume that each customer independently abandons the queue, or reneges, if his service has not begun within a certain amount of time, which could be a random variable drawn from a given distribution. Many papers have studied such queueing systems with reneging customers from a performance evaluation standpoint; see, for example, Afanas'eva [1], Baccelli et al [3], Daley [11], Garnett et al [12], Kovalenko [21], Lillo and Martin [25], Palm [29], Reed and Ward [32], Stanford [35], Ward and Glynn [37,38], and Zeltyn and Mandelbaum [41]. In particular, a lot is known about the behavior of these systems in asymptotic parameter regimes, such as the heavy-traffic regime for a queue with a single server (Ward and Glynn [37,38], Reed and Ward [32]), as well as the many-server regime (Garnett et al [12], Zeltyn and Mandelbaum [41]).…”
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confidence: 99%
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“…Daley [7], [8] studied the distribution of the stationary waiting time of the GIIG/I model. (See also [1] and [2].) In this paper, we shall obtain a fairly complete solution for the GIIG/I model.…”
Section: Introductionmentioning
confidence: 99%
“…Investigations of the G1/G / 1 system with a general reneging distribution appear to have begun with a model proposed by Kovalenko (1961). Necessary and sufficient conditions for existence of a limiting distribution for the waiting time in a G1/G / 1 queue in which the customer's wait is bounded by a random variable are given in Afanas'eva (1965). Daley (1965) also gives conditions for the existence of the limiting waiting time distribution, and derives an integral equation for the distribution.…”
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confidence: 99%