Simple bounds for queueing systems with breakdowns

Computationally attractive and intuitively obvious simple bounds are proposed for finite service systems which are subject to random breakdowns. The services are assumed to be exponential. The up and down periods are allowed to be generally distributed. The bounds are based on product-form modifications and depend only on means. A formal proof is presented. This proof is of interest in itself. Numerical support indicates a potential usefulness for quick engineering and performance evaluation purposes

The M/M/c with critical jobs

We consider the M/M/c queue, where customers transfer to a critical state when their queueing (sojourn) time exceeds a random time. Lower and upper bounds for the distribution of the number of critical jobs are derived from two modifications of the original system. The two modified systems can be efficiently solved. Numerical calculations indicate the power of the approach

Bounds for performance characteristics : a systematic approach via cost structures

In this paper we present a systematic approach to the construction of bounds for the average costs in Markov chains with possibly infinitely many states. The technique used to prove the bounds is based on dynamic programming. Most performance characteristics of Markovian systems can be represented by the average costs for some appropriately chosen cost structure. Therefore, the approach can be used to generate bounds for relevant performance characteristics. The approach is demonstrated for the shortest queue model. It is shown how for this model several bounds for the mean waiting time can be constructed. We include numerical results to demonstrate the quality of these bound