 Poisson arrival process (M), general service time distribution (G), R servers and an infinite number of waiting positions in the system, and each server applies the Processor Sharing (PS) service discipline. As mentioned above, M/G/R-PS model is applied in cases when the transmission rate of each flow is limited to a peak rate rpeak , which is lower than the link capacity C (i.e. rpeak < C). Then the shared link appears as a processor sharing system with R = C/rpeak servers. 6.3 Dimensioning for Elastic Traffic flow 1 Arrivals (A) Departures Infinite Buffer Places flow n Arrival Process - Poisson process R Servers (Processor Sharing service discipline) Figure 6.17. Illustration of M/G/R-PS Model For an M/G/R-PS model where R = C/rpeak, the expected sojourn time (or average transfer time) E{T(x)} for an object of size x is given by [Lin99]: (6.18) Here, parameter p denotes the mean traffic load (or utilization on the link). It can be derived from the mean flow arrival rate he and mean object size le by = E2 represents Erlang's second formula (Erlang C formula) with R servers and A=Rp = as given in equation (6.19). It is known that the Erlang C formula calculates the delay probability (i.e. the probability that a job has to wait) of Erlang's delay system denoted as M/M/n [Ive04]. The given equation is only exact, if R is an integer value. However, for fractional R a continuous approximation for the Erlang function is given in [FK78]. (6.19) In the equation (6.18), it can be obviously seen that the minimum time for transferring a file of size X is equal to x / peak This minimum transfer time is achieved, if at most R flows are sending data. Every additional flow, which becomes active during the transfer process, takes away bandwidth and thus prolongs the transfer. The resultant additional delay is a consequence of the rate reduction imposed by processor sharing, since more than R flows are active. The part for the expected prolongation of the average transfer time in equation (6.18) is called delay factor fr: (6.20