Many-server diffusion limits for G/Ph/n+GI queues
By J. Dai, Shuangchi He, Tolga Tezcan. 2010
97 citations recorded by the source corpus.
This paper studies many-server limits for multi-server queues that have a phasetype service time distribution and allow for customer abandonment. The rst 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 patience time distribution is restricted to be exponential. We prove that a pair of diusion-scaled total-customer-count and server-allocation processes, properly centered, converges in distribution to a continuous Markov process as the number of servers n goes to innity. In the overloaded case, the limit is a multi-dimensional diusion process, and in the critically loaded case, the limit is a simple transformation of a diusion process. When
Subfields: Management Information Systems, Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/5d4b841662eeb9e118bd8e3277871a0cf9f737f9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Management Information Systems
In Management Science and Operations Research
In Statistics and Probability
Citations in the corpus
- Diffusion models and steady-state approximations for exponentially ergodic Markovian queues. (2014, background): “,0)′, corresponding to all customers commencing their service at phase 1 (the diffusion limits in [8] cover the general case where p is an arbitrary probability vector).”
- Stein's method for steady-state diffusion approximations: an introduction through the Erlang-A and Erlang-C models (2015, background): “Proving such limit theorems has been an active area of research in the last 50 years; see, for example, [7, 8, 37, 38, 33, 51] for single-class queueing networks, [49, 9, 63] for multiclass queueing networks, [42, 64] for bandwidth sharing networks, [32, 50, 17] for many-server queues.”