Self-Service System with Rating Dependent Arrivals

Abstract

A multi-server infinite buffer queueing system with additional servers (assistants) providing help to the main servers when they encounter problems is considered as the model of real-world systems with customers’ self-service. Such systems are widely used in many areas of human activity. An arrival flow is assumed to be the novel essential generalization of the known Markov Arrival Process (MAP) to the case of the dynamic dependence of the parameters of the MAP on the rating of the system. The rating is the process defined at any moment by the quality of service of previously arrived customers. The possibilities of a customers immediate departure from the system at the entrance to the system and the buffer due to impatience are taken into account. The system is analyzed via the use of the results for multi-dimensional Markov chains with level-dependent behavior. The transparent stability condition is derived, as well as the expressions for the key performance indicators of the system in terms of the stationary probabilities of the Markov chain. Numerical results are provided.

Analysis of Queueing System with Dynamic Rating-Dependent Arrival Process and Price of Service

“…The influence of ratings on the performance of different service providers accounting for possible congestion is widely analyzed in the vast existing literature; see, e.g., [2][3][4][5][6][7][8][9][10][11][12][13].…”

“…In [9], specific guidelines are provided for managerial interventions to improve service quality and guests' satisfaction for each grading category in hotels in South Africa whose star grading differs. In [10], the multi-server queueing model with additional servers (assistants) providing help to the main servers when they encounter problems is considered a model of real-world systems with customers' self-service. An arrival flow is assumed to be the essential generalization of the known Markov arrival process in the case of the dynamic dependence of the parameters on the rating of the system.…”

“…The comparative rating of two providers is introduced, and customers make a choice between two providers based on this rating. The possibility of increasing the revenue of the service provider via a suitable price alteration corresponding to the change in the rating, which is the focus of the current paper, was not explored in [10,11]. A few summaries of the pertinent literature are available in all the mentioned papers, as well as in [12].…”

Stalling in Queuing Systems with Heterogeneous Channels

“…In [22], a finite-source queueing system serving one class of customers and consisting of heterogeneous servers with unequal service intensities and of one common queue were investigated. The authors of [23] provided an analysis of the dependence of the convergence of experimental results on the type of distribution used by the system parameters in heterogeneous queueing resource system with an unlimited number. In [24], a multi-server infinite buffer queueing system with additional servers (assistants) providing help to the main servers when they encountered problems was analysed through multi-dimensional Markov chains.…”

Queueing System with Potential for Recruiting Secondary Servers

“…Also, a few practical examples dealing with managerial decision are presented. In [24], a multi-server infinite buffer queueing system with additional servers (assistants) provides help to the main servers whenever the server encounters problems that are commonly noticed in real-world situations.…”