TELCOM 2120 Network Performance Homework 5 Spring 04
Due March 24
1. For the random number generator below
(a) Compute Zi and Ui for enough values of i to cover an entire cycle
(b) Plot a scatter diagram of the Zi values 1 apart
(c) Compute the mean value of Ui across 1 cycle
Zi = (11Zi-1)(mod 16) with Z0 = 7
2. Using the inverse transform method develop a generator for the random variable with
distribution function . Use the first three Ui values from part (a) of problem 1 to create 3
values from the random variable below.
F(x) = (x2)/9 0 < x < 3
3. Using any of the single server queue program discussed in class (C, CSIM, OPNET, EZSIM,
NS, COMNET), to simulate the queue for the case of exponentially distributed interarrivals with
mean interarrival time 1 and exponentially distributed service times with mean service time 0.8
Using the replication deletion approach, (a) make 10 runs each 100 seconds in length after the
initial transient and determine a 90% confidence interval on the mean delay in the system,
determine the relative precision of the confidence interval. (b) repeat part (a) but make each run
5000 seconds in length after the initial transient.
4. Consider a telephone system where a large group of phones are connected through a PBX to a
central office via a T1 line which can handle 24 simultaneous phone calls. During the busy hour,
calls arrive to the PBX according to a Poisson process with a mean rate of co per hour destined
for the central office. The phone calls are exponentially distributed in length with mean 1/
minutes per call. Construct a simulation model of the system, using the replication/deletion
approach determine a 90% confidence interval with a relative precision of less than or equal to
10% on the call blocking for the cases below.
(a) The case ofco = 380, 1/ = 3 and when calls arrive to the PBX for the central office and all
lines to the central office are busy they are blocked and cleared, determine the call blocking rate.
(b) Given the same offered load as part (a), consider the case when, rather than the blocked call
attempts disappearing from the system, each blocked call retries after an exponentially
distributed back off time with mean six minutes until it is successful. Using simulation determine
the call blocking rate at the PBX T1 line including call reattempts.
(c) Repeat (b) for the case of deterministic call reattempts with a fixed 1 minute between
reattempts (as might be the case from a PC/modem dialing up a ISP).
