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Sergeeva N. V., Stankevich E. P., Tananko I. E. An approximate method for analyzing a queuing system with batch arrivals and batch services. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2026, vol. 26, iss. 1, pp. 145-155. DOI: 10.18500/1816-9791-2026-26-1-145-155, EDN: XIYXTG
An approximate method for analyzing a queuing system with batch arrivals and batch services
A queueing system with a single server and an infinite-capacity buffer is considered. At any given time, one or two customers with specified probabilities can be received at once. The durations of intervals between arrivals of customers are exponentially distributed random variables. The customers are randomly selected from the buffer and served in batches of a fixed size. Customers are served as a unique batch of a given size with exponentially distributed service time. After the completion of service, the entire batch instantly leaves the system. If a batch of customers is not formed in the system queue at this moment, the server waits until the required number of customers is received by the system. Using the method of probability generating functions, expressions for the stationary probabilities of the system with batch arrivals and batch services are obtained. The average queue size and the average sojourn time in the system are derived. An approximate method for analyzing systems with batch arrivals and batch services based on a queueing system with ordinary arrivals and batch services is proposed. A comparative analysis of the results of calculations of the characteristics obtained using accurate and approximate methods of analysis of the service system under consideration is carried out.
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