2020/08/16 by Gunther, Neil J.
#B.8.2 #C.2.1 #C.2.4 #C.4 #C.5.5 #D.4.8 #Distributed #FOS: Computer and information sciences #Networking and Internet Architecture (cs.NI) #Parallel #Performance (cs.PF) #and Cluster Computing (cs.DC)
paper · doi:10.48550/arxiv.2008.06823
This exposition presents a novel approach to solving an M/M/m queue for the waiting time and the residence time. The motivation comes from an algebraic solution for the residence time of the M/M/1 queue. The key idea is the introduction of an ansatz transformation, defined in terms of the Erlang B function, that avoids the more opaque derivation based on applied probability theory. The only prerequisite is an elementary knowledge of the Poisson distribution, which is already necessary for understanding the M/M/1 queue. The approach described here supersedes our earlier approximate morphing transformation.