# Continuity of the M/G/c queue

@article{Breuer2008ContinuityOT, title={Continuity of the M/G/c queue}, author={Lothar Breuer}, journal={Queueing Systems}, year={2008}, volume={58}, pages={321-331} }

Consider an M/G/c queue with homogeneous servers and service time distribution F. It is shown that an approximation of the service time distribution F by stochastically smaller distributions, say Fn, leads to an approximation of the stationary distribution π of the original M/G/c queue by the stationary distributions πn of the M/G/c queues with service time distributions Fn. Here all approximations are in weak convergence. The argument is based on a representation of M/G/c queues in terms of…

## 2 Citations

The Total Overflow during a Busy Cycle in a Markov-Additive Finite Buffer System

- Computer ScienceMMB/DFT
- 2010

This work considers a finite buffer system where the buffer content moves in a Markov-additive way while it is strictly between the buffer boundaries and determines the joint distribution of the total overflow and the last time of being at the upper boundary.

Markov Chains on Continuous State Space

- Mathematics
- 2010

A piecewise deterministic Markov process is studied, which is applied to deal with more general queues such as the GI/G/c queue and introduces continuousphase type (CPH) distribution and continuous-phase Markovian arrival process (CMAP), and then analyze a CMAP/CPH/1 queue.

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