Blocking and Delays in M⁽ⁿ⁾/M/c Bulk Queuing Systems

The current literature on the subject of queuing systems has included the analytical study of systems with bulk arrivals. Heretofore, all analyses have been concerned with single server systems only. This paper presents results for queuing systems with bulk arrivals; the particular systems are characterized by Poisson arrival epochs with n arrivals at each epoch, exponential service times and c servers. The probability of blocking for both loss and delay systems are investigated. In addition, the average delay, the variance of the delay, and the delay distribution for first-come-first-served delay systems are presented. Special cases are indicated and numerical aspects of the computation are discussed.