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Asymptotics for the late arrivals problem.
- Source :
- Mathematical Methods of Operations Research; Dec2018, Vol. 88 Issue 3, p475-493, 19p, 3 Graphs
- Publication Year :
- 2018
-
Abstract
- We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays ξi. We describe the model as a bivariate Markov chain, prove its ergodicity and study the joint equilibrium distribution. We write a functional equation for the bivariate generating function, finding the solution on a subset of its domain. This solution allows us to prove that the equilibrium distribution of the chain decays super-exponentially fast in the quarter plane. We exploit the latter result and discuss the numerical computation of the solution through a simple yet effective approximation scheme in a wide region of the parameters. Finally, we compare the features of this queueing model with the standard M / D / 1 system, showing that the congestion turns out to be very different when the traffic intensity is close to 1. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14322994
- Volume :
- 88
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Mathematical Methods of Operations Research
- Publication Type :
- Academic Journal
- Accession number :
- 133378627
- Full Text :
- https://doi.org/10.1007/s00186-018-0643-3