Abstract
A multi-server retrial queue with a hyper-exponential service time is considered in this paper. The study is performed by the method of asymptotic diffusion analysis under the condition of long delay in orbit. On the basis of the constructed diffusion process, we obtain approximations of stationary probability distributions of the number of customers in orbit and the number of busy servers. Using simulations and numerical analysis, we estimate the accuracy and applicability area of the obtained approximations.
Highlights
Nowadays, retrial queues (RQ) are very popular mathematical models of various real systems.These may be call centers [1,2] where a calling customer, if he or she find all operators busy, tries to make a new call again after some time
Consider a retrial queue with N servers and Poisson arrivals with intensity λ
For our purposes of analyzing applicability area of results Equations (51)–(54), let us consider a retrial queue with five servers (N = 5) and hyper-exponential service time with parameters μ1 = 0.5, μ2 = 3, q1 = 0.4, q2 = 0.6
Summary
Retrial queues (RQ) are very popular mathematical models of various real systems. We see great opportunities in using multi-server retrial queues for modeling and design data processing systems with high-intensity data flows [6,7]. The most authors use numerical methods, approximations or even simulation methods to study more complex retrial queues [13,14,15,16,17] This applies to multi-server models [16] including systems with non-exponential service time [13]. Mathematics 2020, 8, 531 probability distributions of the number of customers in the orbit that are applicable in appropriate conditions Unlike these previous works, in this paper, we apply a new approach—The asymptotic diffusion method [22]—To perform more detailed and accurate analysis of the model.
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