Knessl, C.; Matkowsky, B. J.; Schuss, Z.; Tier, C. Distribution of the maximum buffer content during a busy period for state-dependent M/G/1 queues. (English) Zbl 0618.60093 Commun. Stat., Stochastic Models 3, 191-226 (1987). We consider M/G/1 queues characterized by the total unfinished work (buffer content) U(t) in the system at time t. We allow the rate of the Poisson arrivals as well as the rate at which the server works, to depend on the instantaneous value of U(t). In addition, the service density depends on the value of U(t) at the instant that the customer enters the system. We consider systems with a large arrival rate and small mean service times. We then construct asymptotic approximations to the probability that U(t) reaches the level K before completing the current busy period and we also compute the distribution of the maximum of U(t) during a busy period. Cited in 1 Document MSC: 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research Keywords:distribution of the maximum buffer content; Poisson arrivals; asymptotic approximations; busy period PDFBibTeX XMLCite \textit{C. Knessl} et al., Commun. Stat., Stochastic Models 3, 191--226 (1987; Zbl 0618.60093) Full Text: DOI