Asymptotic behavior of loss probability in GI/M/1/K queue as K tends to infinity

摘要

We consider GI/M/l/K queueing system where interarrival times are independent and identically distributed with general distribution, and service times are independent and exponentially distributed. We denote by A the generic random variable representing an interarrival time, by λ{sup}(-1) mean of A and by A{sup}* (s) Laplace-Snelijes transform of A. The service times of customers are independent and exponentially distributed with mean μ{sup}(-1). The offered load p is p =λ/μ. This system has finite buffer of size K to store incoming customers, including the one position for server.