Analysis of an MMAP/PH1, PH2/N/∞ queueing system operating in a random environment

Abstract

Abstract A multi-server queueing system with two types of customers and an infinite buffer operating in a random environment as a model of a contact center is investigated. The arrival flow of customers is described by a marked Markovian arrival process. Type 1 customers have a non-preemptive priority over type 2 customers and can leave the buffer due to a lack of service. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. The criterion of ergodicity for a multi-dimensional Markov chain describing the behavior of the system and the algorithm for computation of its steady-state distribution are outlined. Some key performance measures are calculated. The Laplace-Stieltjes transforms of the sojourn and waiting time distributions of priority and non-priority customers are derived. A numerical example illustrating the importance of taking into account the correlation in the arrival process is presented

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 21 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.