Abstract
In the present paper, the infinite-server queue model \(MMAP_{k}(t)|G_{k}|\infty \) in transient MMAP random environment with time varying marked MAP arrival of k types of customers subject to catastrophes is considered. The transient joint probability generating functions (PGF) of the number of different types of customers present in the model at moment t and the number of different types of customers departing from the system in the time interval (0, t] are found. The Laplace-Stieltjes transform (LST) of total volume of customers being in service at moment t is defined. The basic differential equations for joint probability generating functions of the number of busy servers and served customers for transient and stationary random environment are obtained.
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This work was supported by “Data Science Program with Career Support and Connections to Industry,” NSF Award 1842386 grant.
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Kerobyan, R., Kerobyan, K., Shubin, C., Nguyen, P. (2020). Infinite-Server Queue Model \(MMAP_{k}(t)|G_{k}|\infty \) with Time Varying Marked Map Arrivals of Customers and Occurrence of Catastrophes. In: Gaj, P., Gumiński, W., Kwiecień, A. (eds) Computer Networks. CN 2020. Communications in Computer and Information Science, vol 1231. Springer, Cham. https://doi.org/10.1007/978-3-030-50719-0_13
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