SINGLE USER RESERVATION SYSTEM The residual service time is the same as in the vacation case R=λ EⅨ(1pEFV2 2 2EIV Hence EX 2]+ E(V1.EMM 2(1-p)2EV If all reservation intervals are of constant duration a EⅨ21]AA
SINGLE USER RESERVATION SYSTEM • The residual service time is the same as in the vacation case, R = λ E[X2] + (1-ρ)E[V2] 2 2 E[V] • Hence, W = λ E[X 2] + E[V 2] + E[V] 2(1- ρ ) 2 E[V] 1- ρ • If all reservation intervals are of constant duration A, W = λ E[X 2] + A 2(1- ρ ) 1- ρ 2 + A Eytan Modiano Slide 6
Multi-user exhaustive system Consider m incoming streams of packets, each of rate n/m Service times X] are lID and independent of arrivals with mean 17) second moment E[XI Server serves all packets from stream 0, then all from stream 1 then all from m-1. then all from 0, etc There is a reservation interval of fixed duration vi=V(for all Arrival from stream o Time→> Stream Stream 1 Stream 2 Stream 0
Multi-user exhaustive system • Consider m incoming streams of packets, each of rate λ/m • Service times {X n} are IID and independent of arrivals with mean 1/ µ, second moment E[X 2]. • Server serves all packets from stream 0, then all from stream 1, ..., then all from m-1, then all from 0, etc. • There is a reservation interval of fixed duration Vi = V (for all i) Arrival from stream 0 W Time -> m = 3 V0 V 1 V2 V 0 V1 V 2 Stream 0 Stream 1 Stream 2 Stream 0 Eytan Modiano Slide 7