. M/ M/c queue (c ≥ 1): transient state distribution.

Suppose that k(≥1) customers are already present at time to = 0 and that the nth new customer arrives at time t, (n ≥ 1).

Denote X, = number of customers present at time t, + 0

(including the nth arrival at tn).

Pk(n, i) = Pr{X, = i| number present at time to(=0) is k}

p=X/cu (which need not be <1).

(The first arriving customer at t1 need not find k customers present but will find j (0 ≤ j ≤ k) customers.)

(See Kelton and Law (1985), who also consider the implication for steady-
state simulation.)