Analysis of a Queueing Model with MAP Arrivals and Heterogeneous Phase-Type Group Services

Srinivas R. Chakravarthy ()
Additional contact information
Srinivas R. Chakravarthy: Department of Industrial and Manufacturing Engineering and Mathematics, Kettering University, Flint, MI 48504, USA

Mathematics, 2022, vol. 10, issue 19, 1-30

Abstract: Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into two sectors: manufacturing and service. These two sectors cover everything we deal with on a day-to-day basis. Queues in which the services are offered in blocks (or groups or batches) are well established in the literature and have a wide variety of applications in practice. In this paper, we look at one such queueing model in which the arrivals occur according to a Markovian arrival process and the services are offered in batches of varying sizes from 1 to a finite pre-determined constant, say, b . The service times are assumed to be of phase type with representation depending on the size of the group. Thus, the distributions considered are heterogeneous from both the representation and rate points of view. The model can be studied as a G I / M / 1 -type queue or as a Q B D -model. The model is analyzed in steady state by establishing results including on the rate matrix and the waiting time distribution and providing a number of illustrative examples.

Keywords: queueing model; Markovian arrivals; phase type service; QBD process; matrix-analytic methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/19/3575/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/19/3575/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:19:p:3575-:d:930381

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().