Average residual service Time (with vacations) Residual service Time R(t) X 4 time M(t) R=[R()= (τ)d 2 2 R=imE/N(]EⅨ L(t EV 2 Where l(t is the number of vacations taken up to time t M(t) is the number of customers served by time tAverage Residual Service Time (with vacations) Residual Service Time R(t) X X X X 1 2 3 V 4 1 X1 X2 V1 X3 X4 time -> 0 t M(t) 2 L(t) 2 R = [R(t)]= 1 R( τ )d τ = 1 (� X i + � V j ) t t 2 2 i=1 j=1 R = lim E[M(t)] E[X 2] + L(t) E[V 2] t →∞ t 2 t 2 • Where L(t) is the number of vacations taken up to time t • M(t) is the number of customers served by time t Eytan Modiano Slide 8