Analysis of bulk networks under high loads (Q1816018)

A bulk stochastic queueing network (BSQN) is a network whose nodes are concentrators (``stations'') that receive random streams of customers from external sources and are served by mobile multichannel servers (``vehicles''). As the simplest BSQN we analyze an elementary network (EBSQN) with the following properties: it consists of a finite munber \(N\) \((1\leq N<\infty)\) of stations connected in a series; vehicles from an external source arrive in a free state at the first station; the service of all customers in the vehicle is completed at the last station, and the vehicle leaves the EBSQN. The notion of BSQN was introduced by the author [Kibernetika, Kiev 1977, No. 1, 117-125 (1977; Zbl 0365.90066); Cybernetics 21, 662-670 (1985), translation from Kibernetika 1985, No. 5, 81-86 (1985; Zbl 0612.60084); Autom. Remote Control 47, 943-951 (1986), translation from Avtom. Telemekh. 1986, No. 7, 78-85 (1986; Zbl 0613.90023); ibid. 50, No. 3, 355-365 (1989) resp. ibid. 1989, No. 3, 84-98 (1989; Zbl 0683.90029); and ``Elements of the theory of bulk stochastic queueing networks and its applications'' (1990; Zbl 0783.60096)], where the elementary theory of bulk networks was developed systematically. The present study is a continuation of the cited papers. It examines the asymptotic behavior of the queue length and the waiting time of customers in the network stations under a high load. The network is assumed to operate in a stationary mode.