The transient blocking probabilities in M/M/N loss systems via large deviations

Hitting probabilities and large deviations

Let ”Yn•n∈Z+ be a sequence of random variables in R d and let A ⊂ Rd: Then P”Yn ∈ A for some n• is the hitting probability of the set A by the sequence ”Yn•. We consider the asymptotic behavior, as m → ∞, of P”Yn ∈ mA; some n• = P”hitting mA• whenever (1) the probability law of Yn/n satisfies the large deviation principle and (2) the central tendency of Yn/n is directed away from the given set ...

Bounds for the Loss Probabilities of Large Loss Queueing Systems

The aim of this paper is to establish the bounds for the least root of the functional equation x = b G(μ − μx), where b G(s) is the Laplace-Stieltjes transform of an unknown probability distribution function G(x) of a positive random variable having the first two moments g1 and g2, and μ is a positive parameter satisfying the condition μg1 > 1. The additional information characterizing G(x) is ...

2078 Hitting Probabilities and Large Deviations

Transient handover blocking probabilities in road covering cellular mobile networks

This paper investigates handover and fresh call blocking probabilities for subscribers moving along a road in a traffic jam passing through consecutive cells of a wireless network. It is observed and theoretically motivated that the handover blocking probabilities show a sharp peak in the initial part of a traffic jam roughly at the moment when the traffic jam starts covering a new cell. The th...

A large deviations approach to the transient of the Erlang loss model

This paper deals with the transient behavior of the Erlang loss model. After scaling both arrival rate and number of trunks, an asymptotic analysis of the blocking probability is given. Apart from that, the most likely path to blocking is given. Compared to Shwartz and Weiss [14], more explicit results are obtained by using probabilistic arguments. The computation method is applied to the probl...