Abstract
The operation of many real-world systems, e.g., servers of data centers, is accompanied by the heating of a server. Correspondingly, certain cooling mechanisms are used. If the server becomes overheated, it interrupts processing of customers and needs to be cooled. A customer is lost when its service is interrupted. To prevent overheating and reduce the customer loss probability, we suggest temporal termination of service of new customers when the temperature of the server reaches the predefined threshold value. Service is resumed after the temperature drops below another threshold value. The problem of optimal choice of the thresholds (with respect to the chosen economical criterion) is numerically solved under quite general assumptions about the parameters of the system (Markovian arrival process, phase-type distribution of service time, and accounting for customers impatience). Numerical examples are presented.
Highlights
The goal of operation of many real-world systems is to obtain profit via providing service to some customers
To maximize the profit, it is necessary to use the power of the available server to a maximum extent. This may cause overheating of the server, the loss of a customer who was using the service during the overheating moment and a temporal termination of the service for cooling the server
A novel in the literature queueing model is considered. This model considers the possible heating of a server during the service process that causes the necessity of its permanent cooling
Summary
The goal of operation of many real-world systems is to obtain profit via providing service to some customers. Under any fixed pair of thresholds, the behavior of the system is described by a Markov chain This Markov chain is multi-dimensional because it has to include the components defining the number of customers in the system, the current state of the server (idle, operating, or cooling) and its temperature, underlying processes of customer arrival and service processes. Having the stationary probabilities computed, we derive formulas for computation of the main performance indicators of the system and the cost criterion for any fixed pair of the thresholds defining behavior of the system This allows us to numerically solve the problem of choosing the optimal values of the thresholds.
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