Find the mean system time of a customer

Reference no: EM131920882

Question: 1. Let us model a router by an M/M/1 system with mean service time equal to my = 0.5 s.

a) How many packets per second can be processed for a given mean system time of 2.5 s?

b) What is the increase in mean system time if the arrival rate increases by 10%?

2. Consider a system with an infinite population of users. Each user can be in two states, namely idle and active. In the idle state, a user does not perform any action. In the active state, the user transmits one packet over a shared transmission channel. When the packet transmission is completed the user leaves the system. Users activate in a Poisson fashion, that is, the time intervals between successive users activations are iid rvs with exponential distribution of parameter λ. The channel has a bit rate of Rb bit/s, which is equally divided among all the active users. The transmission rate of any active user at time t will be equal to

r(t) = R_b/x(t)

where x(t) denotes the number of active users at time t. Each packet has a random size with exponential distribution and mean L. Find what follows.

a) The stationary PMD and mean of x(t) and the system stability conditions.

b) The mean system time of a customer.

c) Assuming that, after user U becomes active, the system stops accepting new users, that is, no other users are allowed to activate. Find the mean time after which user U completes its transmission.

Reference no: EM131920882

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