Fig. 1. Various time epochs in late arrival system with delayed access.

Fig. 2. Effect of buffer size (N) on the probability that the server is busy (ρ^′), when service time is deterministic with mean E(S)=5 and vacation time is geometric with mean E(V)=20.

Fig. 3. Effect of buffer size (N) on the blocking probability (), when service time is geometric with mean E(S)=3.3333 and vacation time is geometric with mean E(V)=5.

Fig. 4. Effect of average vacation time (E(V)) on the average waiting time (W_q), when service time is geometric with mean E(S)=3.3333, N=10 and vacation time is deterministic.

Fig. 5. Effect of buffer size (N) on the blocking probability (), when service time is deterministic with mean E(S)=4 and vacation time is deterministic with mean E(V)=7.

Queue-length distributions at various epochs in the case of a single vacation when service and vacation times are deterministic with ρ=1.6667, λ^*=0.3333, s₅=1, v₃=1, N=10, m=2

..

Queue-length distributions at various epochs in the case of a single vacation when service and vacation times are geometric with ρ=0.8399, λ^*=0.0924, E(S)=0.9090, E(V)=5.0000, N=60, m=7

.

Queue-length distributions at various epochs in the case of multiple vacations when service and vacation times are arbitrary with ρ=0.6097, λ^*=0.0924, s₅=0.6, s₉=0.4, v₂=0.2, v₅=0.3, v₇=0.5, N=10, m=7

.

Queue-length distributions at various epochs in the case of multiple vacations when service and vacation times are geometric with ρ=1.1111, λ^*=0.3333, E(S)=3.3333, E(V)=5.0000, N=10, m=2

.