Single user gated system (cont. Waiting time in the single user gated systems W,=R+∑X,+ ● S0, W=R+No/u+EV]3W=(R+EV)/(1-P) And the residual time is the same as in the vacation case R=ix.(-e) 2 2V ·Hence, X2 2 W= 21-p+2+1-p Weigiang Sun Communication Networks 6
Weiqiang Sun Communication Networks Single user gated system (cont.) 6 W R X V i i i i W R N E V Q / 2 2 1 2 2 X V R V • Waiting time in the single user gated systems • So, W R E V / 1 • And the residual time is the same as in the vacation case • Hence, 2 2 2(1 ) 1 2 X V V W V
Multi-user systems ·Assume 一 m incoming streams,each of rate A/m 一 Service times are i.i.d and independent of arrivals with mean 1/u,second moment E[X2] Server serves all packets from stream 1,then all packets from stream 2 and so on... Fixed reservation interval Vi =V(for all i),but data transmission intervals are not fixed Packet i from stream 3 arrives Start of packet i transmission R3 R1 R2 R3 R1 长 Residual Packets in queue to wait for Reservation intervals to wait for Weigiang Sun Communication Networks
Weiqiang Sun Communication Networks Multi-user systems • Assume – m incoming streams, each of rate λ/m – Service times are i.i.d and independent of arrivals with mean 1/μ, second moment E[X2 ] – Server serves all packets from stream 1, then all packets from stream 2 and so on… – Fixed reservation interval Vi = V (for all i), but data transmission intervals are not fixed 7 R3 R1 R2 R3 R1 Packet i from stream 3 arrives Start of packet i transmission Residual Packets in queue to wait for Reservation intervals to wait for