Pseudo Steady-State Period in Non-Stationary Infinite-Server Queue with State Dependent Arrival Intensity

Anatoly Nazarov, Alexander Dudin and Alexander Moiseev
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Anatoly Nazarov: Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia
Alexander Dudin: Faculty of Applied Mathematics and Informatics, Belarusian State University, 220030 Minsk, Belarus
Alexander Moiseev: Institute of Applied Mathematics and Computer Science, Tomsk State University, 634050 Tomsk, Russia

Mathematics, 2022, vol. 10, issue 15, 1-12

Abstract: An infinite-server queueing model with state-dependent arrival process and exponential distribution of service time is analyzed. It is assumed that the difference between the value of the arrival rate and total service rate becomes positive starting from a certain value of the number of customers in the system. In this paper, time until reaching this value by the number of customers in the system is called the pseudo steady-state period ( P S S P ). Distribution of duration of P S S P , its raw moments and its simple approximation under a certain scaling of the number of customers in the system are analyzed. Novelty of the considered problem consists of an arbitrary dependence of the rate of customer arrival on the current number of customers in the system and analysis of time until reaching from below a certain level by the number of customers in the system. The relevant existing papers focus on the analysis of time interval since exceeding a certain level until the number of customers goes down to this level (congestion period). Our main contribution consists of the derivation of a simple approximation of the considered time distribution by the exponential distribution. Numerical examples are presented, which confirm good quality of the proposed approximation.

Keywords: infinite-server queue; non-stationary regime; steady-state period; asymptotic analysis (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)

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