Matched Queues with Flexible and Impatient Customers

We consider a multi-server queueing system with a visible queue and an arrival flow that is dynamically dependent on the system’s rating. This rating reflects the level of customer satisfaction with the quality and price of the provided service. A higher rating implies a higher arrival rate, which motivates the service provider to increase the price of the service. A steady-state analysis of this system using the proposed mechanism for changing the rating and a threshold strategy for changing the price is performed. This is carried out via the consideration of a suitably constructed multidimensional Markov chain. The impact of the variation in the threshold defining the strategy for changing the price on the key performance indicators is numerically illustrated. The results can be used to make managerial decisions, leading to an increase in the effectiveness of system operations.

Section: Customersmentioning

confidence: 99%

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

D’Apice,

Dudin,

Dudina

et al. 2024

“…In the context of sensor networks, impatience is caused by the useless transmission of a signal to the coordinating node of the network due to the obsolescence of information contained in this signal. Lists of related research on queues with impatient demands can be found, e.g., in recent papers [34][35][36][37][38][39]. Account of the impatience frequently causes essential complications in the analysis because the behavior of the random process describing the dynamics of the system becomes level-dependent and the corresponding process does not belong to the classes of QBD processes or M/G/1and GI/M/1-type structures that Markov chains were used to exhaustively investigate by M. Neuts, see [40,41].…”

Section: Queuing Systems With Demand Impatiencementioning

confidence: 99%

Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers

D’Apice,

D’Arienzo,

Dudin

et al. 2023

A queuing system having two different servers is under study. Demands enter the system according to a Markov arrival process. Service times have phase-type distribution. Service of demands is possible only if the fixed number of energy units, probably different for two servers, is available in the system at the potential service beginning moment. Energy units arrive in the system also according to a Markov arrival process and are stored in a stock (battery) of a finite capacity. Leakage of energy units from the stock can occur. Demands waiting in the infinite buffer are impatient and can leave the buffer after an exponentially distributed waiting time. One server is the main one and permanently provides service when the buffer is not empty and the required number of energy units is available. The second server is the assistant server and is switched on or off depending on the availability of energy units and queue length according to the hysteresis strategy defined by two thresholds. The assistant server is switched on when the queue length is not less than the greater threshold and is switched off when the queue length becomes smaller than the smaller threshold. The use of the assistant server has to be paid. Thus, the problem of the optimal selection of the thresholds defining the control strategy naturally arises. To solve this problem, the study of the behavior of the system under any fixed values of the parameters of the control strategy is necessary. Such a study is given in this paper. Numerical results are presented. They illustrate the feasibility of computer realization of the developed algorithms for computation of the stationary distribution of the system states and the main key performance indicators as well as the result of solving one of the possible optimization tasks.

“…In retail networks and health systems (such as blood banks or organ transplantation hospitals), impatience is explained by the restricted term of the suitability of the items required for service. Recent lists of related research on queues with impatient customers can be found, e.g., in [58][59][60][61].…”

Section: Introductionmentioning

confidence: 99%

Randomized Threshold Strategy for Providing Flexible Priority in Multi-Server Queueing System with a Marked Markov Arrival Process and Phase-Type Distribution of Service Time

Dudin

Dudina

2023

In this paper, we analyze a multi-server queueing system with a marked Markov arrival process of two types of customers and a phase-type distribution of service time depending on the type of customer. Customers of both types are assumed to be impatient and renege from the buffers after an exponentially distributed number of times. The strategy of flexible provisioning of priorities is analyzed. It assumes a randomized choice of the customers from the buffers, with probabilities dependent on the relation between the number of customers in a priority finite buffer and the fixed threshold value. To simplify the construction of the underlying Markov chain and the derivation of the explicit form of its generator, we use the so-called generalized phase-type distribution. It is shown that the created Markov chain fits the category of asymptotically quasi-Toeplitz Markov chains. Using this fact, we show that the considered Markov chain is ergodic for any value of the system parameters and compute its stationary distribution. Expressions for key performance measures are presented. Numerical results that show how the parameters of the control strategy affect the system’s performance measurements are given. It is shown that the results can be used for managerial purposes and that it is crucial to take correlation in the arrival process into account.