LOSSES IN M/GI/m/n QUEUES
نویسنده
چکیده
The M/GI/m/n queueing system with m homogeneous servers and the finite number n of waiting spaces is studied. Let λ be the customers arrival rate, and let μ be the reciprocal of the expected service time of a customer, where λ = mμ. The paper proves that under this assumption the expected number of losses during a busy period remains the same for all n ≥ 1, while in the particular case of the Markovian system M/M/m/n the expected number of losses during a busy period is m m m! for all n ≥ 0. Under the additional assumption that the probability distribution function of a service time belongs to the class NBU or NWU, the paper establishes simple inequalities for those expected numbers of losses in M/GI/m/n queueing systems.
منابع مشابه
Error Bounds for Perturbing Nonexponential Queues
A general framework is provided to derive analytic error bounds for the effect of perturbations and inaccuracies of nonexponential service or arrival distributions in singleand multi-server queues. The general framework is worked out in detail for the three types of finite or infinite buffer queues: GI/G/1/N , M/G/c/N , and GI/M/c/N . First, for the standard GI/G/1/N queue, it is illustrated ho...
متن کاملMany-server diffusion limits for G/Ph/n + GI queues
This paper studies many-server limits for multi-server queues that have a phasetype service time distribution and allow for customer abandonment. The first set of limit theorems is for critically loaded G/Ph/n + GI queues, where the patience times are independent, identically distributed following a general distribution. The next limit theorem is for overloaded G/Ph/n + M queues, where the pati...
متن کاملFluid Models for Multiserver Queues with Abandonments
Deterministic fluid models are developed to provide simple first-order performance descriptions for multi-server queues with abandonment under heavy loads. Motivated by telephone call centers, the focus is on multi-server queues with a large number of servers and non-exponential service-time and time-to-abandon distributions. The first fluid model serves as an approximation for the G/GI/s + GI ...
متن کاملQueues with Many Servers and Impatient Customers
The asymptotic many-server queue with abandonments, G/GI/N +GI , is considered in the qualityand efficiency-driven (QED) regime. Here the number of servers and the offered load are related via the square-root rule, as the number of servers increases indefinitely. QED performance entails short waiting times and scarce abandonments (high quality) jointly with high servers’ utilization (high effic...
متن کاملOn the Relaxation Time for Single Server Queues
This paper gives a natural definition of the relaxation time for general single server queues. First, we describe a GI/GI/I queue as a limit of GI/GPH/I queues. Each GI/GPH/I queue is transferred to some equivalent bulk arrival GIx/M/I queue, which is formulated by a spatially homogeneous Markov chain with reflecting barrior at zero. An upper bound, which is easy to calculate, of the relaxation...
متن کامل