M/G/ Queue with Vacations Useful for polling and reservation systems(e.g, token rings) When the queue is empty, the server takes a vacation Vacation times are lID and independent of service times and arrival times If system is empty after a vacation, the server takes another vacation The only impact on the analysis is that a packet arriving to an empty system must wait for the end of the vacation I arrives ⅤX3X2X1X Time→ R:+ EW]= E[R]+ EDX]ENI =R+Nou=R/(1-p)M/G/1 Queue with Vacations • Useful for polling and reservation systems (e.g., token rings) • When the queue is empty, the server takes a vacation • Vacation times are IID and independent of service times and arrival times – If system is empty after a vacation, the server takes another vacation – The only impact on the analysis is that a packet arriving to an empty system must w ait for t he end of the vacation i arrives Wi Ri Vj X i-3 X i-2 X i-1 Xi Time -> Ni = 3 i-1 W i = R i + � X j j=i￾N i Eytan Modiano Slide 7 E[Wi] = E[Ri] + E[X]E[Ni] = R + N Q/µ = R/(1- ρ)