Stochastic inequalities for an overflow model

Arie Hordijk · Ad Ridder

28 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

A general method to obtain insensitive upper and lower bounds for the stationary distribution of queueing networks is sketched. It is applied to an overflow model. The bounds are shown to be valid for service distributions with decreasing failure rate. A characterization of phase-type distributions with decreasing failure rate is given. An approximation method is proposed. The methods are illustrated with numerical results.

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1986Comparison Methods for Queues and Other Stochastic Models.1984Comparison Methods for Queues and Other Stochastic Models 1982Introduction to Queueing Theory 1985Blocking When Service Is Required From Several Facilities Simultaneously 1983Introduction to Queueing Theory (2nd ed.).1980Continuity of Generalized Semi-Markov Processes 1981Comparing counting processes and queues 1973Warteschlangen

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1993Monotonicity properties of single-server retrial queues 2010Error Bounds and Comparison Results: The Markov Reward Approach For Queueing Networks 1987A formal proof for the insensitivity of simple bounds for finite multi-server non-exponential tandem queues based on monotonicity results

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