Infinite-Server Bulk Queue with MMPP Arrivals

2020 ◽  
pp. 158-170
Author(s):  
Anna Boyarkina ◽  
Svetlana Moiseeva ◽  
Michele Pagano ◽  
Ekaterina Lisovskaya ◽  
Alexander Moiseev
Keyword(s):  
Infinite Server ◽  
Bulk Queue

scholarly journals Perfect sampling for infinite server and loss systems

2015 ◽  
Vol 47 (03) ◽  
pp. 761-786 ◽  
Author(s):  
Jose Blanchet ◽  
Jing Dong
Keyword(s):  
Point Processes ◽  
Marked Point ◽  
Heavy Traffic ◽  
Arrival Rate ◽  
Marked Point Processes ◽  
Perfect Sampling ◽  
Running Time ◽  
Infinite Server ◽  
Loss Systems ◽  
Server System

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.

Stationary Poisson departure processes from non-stationary queues

1986 ◽  
Vol 23 (1) ◽  
pp. 256-260 ◽  
Author(s):  
Robert D. Foley
Keyword(s):  
Poisson Process ◽  
Service Time ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Distribution Functions ◽  
Arrival Process ◽  
Service Time Distribution ◽  
Departure Process ◽  
Infinite Server ◽  
Departure Processes

We present some non-stationary infinite-server queueing systems with stationary Poisson departure processes. In Foley (1982), it was shown that the departure process from the Mt/Gt/∞ queue was a Poisson process, possibly non-stationary. The Mt/Gt/∞ queue is an infinite-server queue with a stationary or non-stationary Poisson arrival process and a general server in which the service time of a customer may depend upon the customer's arrival time. Mirasol (1963) pointed out that the departure process from the M/G/∞ queue is a stationary Poisson process. The question arose whether there are any other Mt/Gt/∞ queueing systems with stationary Poisson departure processes. For example, if the arrival rate is periodic, is it possible to select the service-time distribution functions to fluctuate in order to compensate for the fluctuations of the arrival rate? In this situation and in more general situations, it is possible to select the server such that the system yields a stationary Poisson departure process.

The stability of infinite-server networks with random routing

1989 ◽  
Vol 26 (02) ◽  
pp. 363-371 ◽  
Author(s):  
S. A. Berezner ◽  
V. A. Malyshev
Keyword(s):  
Infinite Number ◽  
Infinite Server ◽  
The Stability ◽  
General Conditions

We consider networks with a very large or infinite number of nodes, linked by cable channels. The request which comes to a node is ordered to occupy a certain route of successive channels. The functioning of the system is regulated by the reserving of channels in order of the arrivals of the requests. Under some general conditions the existence of an ergodic region for such networks is proved. The practical value of the result lies in the fact that these conditions do not depend on the size of the graph.

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