Relation between states observed by arriving and departing customers in bulk systems

AbstractAn important and well known theorem of Queueing Theory establishes the equality of state distributions at arrival and departure epochs, provided that the system state varies by unit jumps. We generalize this result to a class of bulk systems (arrival occur in groups of random size, or departures in groups of fixed size), for which we give a relation between state distributions at arrival and departure instants, under quite general conditions