Approximating service-time distributions by phase-type distributions in single-server queues: a strong stability approach

Djabali, Yasmina; Rabta, Boualem; Aı̈ssani, Djamil

doi:10.1504/ijmor.2018.092107

Cited by 4 publications

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Considering particular PH distributions (exponential, hyperexponential, hypoexponential) and replacing them with the respective explicit form for each of them, we retrieve the results published earlier in [6] and [8] The transition probabilities of the Markov chain X representing the queue length just after the nth departure in the M/M/1 system are given by:…”

Section: Perturbation Boundsmentioning

confidence: 99%

“…For instance, using the moment matching method and matching only the first moment (mean) we use the exponential distribution. If we match the first two moments (mean and coefficient of variation), we could use hyper-or hypoexponential distributions depending on the value of the coefficient of variation as in [7,8], a mixture of two Erlang distributions [23] or a Coxian distribution [18]. Obviously, other possibilities are available since the family of PH distribution is much larger.…”

Section: Introductionmentioning

confidence: 99%

“…In [8], the M/P H/1 queueing model is used to represent an M/G/1 system by approximating the general service time distribution of the latter by a PH distribution. This is achieved by matching the first two moments of both distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Similar results [7] exist for the P H/M/1 queue when perturbing the interarrival time distribution. However, the results in [7,8] are limited in multiple aspects. First, only two specific PH distributions (hypoexponential and hyperexponential) are considered in approximating the underlying general service/interarrival time distribution.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Phase-Type Approximations of Service-Time Distributions in M/G/1 Queues

Rabta

2022

J Math Sci

View full text Add to dashboard Cite

We consider the problem of approximating an M/G/1 queueing system by an M/P H/1 system. Namely, the unknown general service time distribution G is approximated by a phase-type distribution P H. The approximation as well as the estimation of the parameters by means of statistical methods results in perturbations of the system that may affect its performance measures.In this work, we provide by means of the strong stability method, the mathematical justification of the approximation method by phase-type distributions that is already used in several works. We prove the robustness of the underlying Markov chain in each case and estimate an upper bound of the deviation of the stationary vector, resulting from the perturbation of the service-time distribution. We provide numerical examples and compare the perturbation bounds obtained in this paper with the estimates of the real deviation of the stationary vector obtained by simulation.

show abstract

Section: Perturbation Boundsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Phase-Type Approximations of Service-Time Distributions in M/G/1 Queues

Rabta

2022

J Math Sci

View full text Add to dashboard Cite

show abstract

“…However, the scope is primarily focused on theoretic approximations rather than by simulation. [7,12] are two such recent works that consider an underlying process to estimate a general service time distribution in single server and infinite server queues respectively.…”

Section: Handling Incomplete Queue Datamentioning

confidence: 99%

Segmentation analysis and the recovery of queuing parameters via the Wasserstein distance: a study of administrative data for patients with chronic obstructive pulmonary disease

Wilde,

Knight,

Gillard

et al. 2020

Preprint

View full text Add to dashboard Cite

This work uses a data-driven approach to analyse how the resource requirements of patients with chronic obstructive pulmonary disease (COPD) may change, quantifying how those changes impact the hospital system with which the patients interact. This approach is composed of a novel combination of often distinct modes of analysis: segmentation, operational queuing theory, and the recovery of parameters from incomplete data. By combining these methods as presented here, this work demonstrates that potential limitations around the availability of fine-grained data can be overcome. Thus, finding useful operational results despite using only administrative data.The paper begins by finding a useful clustering of the population from this granular data that feeds into a multi-class M/M/c model, whose parameters are recovered from the data via parameterisation and the Wasserstein distance. This model is then used to conduct an informative analysis of the underlying queuing system and the needs of the population under study through several what-if scenarios.The analyses used to form and study this model consider, in effect, all types of patient arrivals and how those types impact the system. With that, this study finds that there are no quick solutions to reduce the impact of COPD patients on the system, including adding capacity to the system. In this analysis, the only effective intervention to reduce the strain caused by those presenting with COPD is to enact external policies which directly improve the overall health of the COPD population before they arrive at the hospital.

show abstract