Blocking When Service Is Required From Several Facilities Simultaneously

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.

Performance analyses of optical burst-switching networks

“…Given the difficulty in obtaining exact mathematical results for this problem, we assume, as in [4], [10], and [17] that each blocking event occurs independently from link to link along any route.…”

“…Since the transformation is decreasing, namely, whenever , the following result is easily derived (as done in [17] for the circuit switching network).…”

Approximations for Call-Blocking Probabilities in Multirouting Multicasting Multirate Loss Networks

“…The idea to the second method originates from a result valid for single slot circuit switched networks proved by Whitt in [19].…”

Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations

“…Our aim is to evaluate the stationary blocking probability of an arbitrary burst and of a burst that is offered to route r. Given the difficulty in obtaining exact mathematical results for this problem, we assume as in [1], [7], [14] and [20] that each blocking event occurs independently from link to link along any route.…”

“…Since the transformation T (B) is decreasing, namely, T (B) < T (B ) whenever B > B , the following result is easily derived (as done in [20] for the circuit switching network).…”