About Busy Period of a Multi-server Queueing Model with Simultaneous Service

This paper investigates the busy period of a multi-server queueing system in which tasks require the simultaneous allocation of a random number of servers.The model considers m, (m 1) homogeneous servers, Poisson arrivals, and exponentially distributed service times.Each task randomly requests between one and m servers for its execution, and service begins only when the required number of servers is available.By formulating the system dynamics using a recursive relation that captures the evolution of the busy period based on task completion and service initiation events.A general expression for the expected busy period is derived.The results contribute to a deeper understanding of multi-server systems with simultaneous service and offer valuable insights for performance evaluation in modern computing infrastructures.