Journal ArticleDOI
On the service system MX/G/∞
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This paper considers the service system MX/G/∞ characterized by an infinite number of servers and a general service time distribution, which is a random variable, the time between group arrivals being exponentially distributed.About:
This article is published in European Journal of Operational Research.The article was published on 1983-06-01. It has received 25 citations till now. The article focuses on the topics: Probability-generating function & Random variable.read more
Citations
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Journal ArticleDOI
On the GIX/G/∞ system
TL;DR: By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases in this paper.
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PORTPLAN, decision support system for port terminals
TL;DR: Models underlying a decision support system for port terminal planning, among others Markov models, queuing models and simple optimization models are considered, give a good insight in this problem field.
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Analysis of an Infinite-Server Queue with Batch Markovian Arrival Streams
Hiroyuki Masuyama,Tetsuya Takine +1 more
TL;DR: This paper considers an infinite-server queue with multiple batch Markovian arrival streams, and derives explicit and numerically feasible formulas for the time-dependent and limiting joint binomial moments of this queue.
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Queueing network MAP−(GI/∞)K with high-rate arrivals
TL;DR: It is shown that the stationary probability distribution of the number of customers at the nodes can be approximated by multi-dimensional Gaussian distribution and an approximation of higher-order accuracy is derived.
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The GR X n /G n /∞ system: system size
Liming Liu,J. G. C. Templeton +1 more
TL;DR: Analytical results are obtained for the generating functions and binomial moments of both the continuous time system size and pre-arrival system size by investigating a general infinite server system with batch arrivals following a Markov renewal input process.
References
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On regenerative processes in queueing theory
TL;DR: In this paper, the stationary distribution of the actual and virtual waiting time of GI/G/1 queues is analyzed. But the authors focus on the residual service time distribution and do not consider the stationary distributions of the idle period and the actual waiting time.
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On infinite server queues with batch arrivals
TL;DR: In this paper, the authors studied the queueing system in which there are an infinite number of servers, all the servers are idle, one server serves only one customer at a time and the service times are independent and identically distributed with distribution function B(t) (t > 0) and mean β(0) and no arrival takes place during (t, t + δt) with the probability 1 − δ t + o(δt).
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The M/M/∞ Queue with Varying Arrival and Departure Rates
T. Collings,C. Stoneman +1 more
TL;DR: The queuing problem of an intensive care unit is discussed and it is shown that it is unlikely that the hourly variation in the arrival rate of patients to the unit will significantly affect the number of beds occupied.