Journal ArticleDOI
Blocking when service is required from several facilities simultaneously
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In this article, a mathematical model of a blocking system with simultaneous resource possession is presented, where each customer requests service from one server in each facility in a subset of the service facilities, with the subset depending on the customer class.Abstract:
This paper analyzes a mathematical model of a blocking system with simultaneous resource possession. There are several multiserver service facilities without extra waiting space at which several classes of customers arrive in independent Poisson processes. Each customer requests service from one server in each facility in a subset of the service facilities, with the subset depending on the customer class. If service can be provided immediately upon arrival at all required facilities, then service begins and all servers assigned to the customer start and finish together. Otherwise, the attempt is blocked (lost without generating retrials). The problem is to determine the blocking probability for each customer class. An exact expression is available, but it is complicated. Hence, this paper investigates approximation schemes.read more
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Improving Service by Informing Customers About Anticipated Delays
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References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
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Probability measures on metric spaces
TL;DR: The Borel subsets of a metric space Probability measures in the metric space and probability measures in a metric group Probability measure in locally compact abelian groups The Kolmogorov consistency theorem and conditional probability probabilistic probability measures on $C[0, 1]$ and $D[0-1]$ Bibliographical notes Bibliography List of symbols Author index Subject index as mentioned in this paper
Journal ArticleDOI
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
TL;DR: Many of the network results of Jackson on arrival and service rate dependencies, of Posner and Bernholtz on different classes of customers, and of Chandy on different types of service centers are combined and extended in this paper.