Spatial M/G/∞ System. Consider a system in which items enter a space S at times T1 ≤ T2 ≤ ... that form a Poisson process with intensity measure μ. The nth item that arrives at time Tn enters S at the...

Spatial M/G/∞ System. Consider a system in which items enter a space S at times T1 ≤ T2 ≤ ... that form a Poisson process with intensity measure μ. The nth item that arrives at time Tn enters S at the location Xn and remains there for a time Vn and then exits the system. Suppose Ft(·) is the distribution of the location in S of an item arriving at time t, and G(t,x)(·) is the distribution of the item’s sojourn time at a location x. More precisely, assume (Xn, Vn) are location-dependent marks of Tn with distributionNext, let D((a, b] × B) denote the number of departures from the set B in the time interval (a, b]. Show that D is a space-time Poisson process on R+ × S and specify E[D((0, t] × B)]