EECS 663

Homework

Performance Analysis

1. A remote switching unit in a PBX has 128 input channels, each with a bit rate of 64 Kb/s for either data or voice transmissions. The remote unit is connected to a non-blocking central switch over a full duplex T1 (24 channel) line. In this application each input channel is used for data transmission. Each message has an average length of 128 bytes. Assuming that the average arrival rate is the same for each input channel, find the maximum average arrival rate so that the blocking probability for the PBX does not exceed PL = 0.01.

2. A data PBX has 24 input channels each at a bit rate of 56 Kb/s. The average input message rate per channel is 10 messages/second and messages are 100 bytes long on average. How many 56 Kb/s output lines are needed to keep the probability of a message being blocked to less the 0.2.

3. How many trunk lines are needed between a PBX and a central office switch to maintain a blocking probability of less than 0.01. Assume that 120 phones are connected to the PBX which generate 0.05 Erlang/phone of busy hour external traffic. What would the blocking probability be if the traffic increased by 50%.

4. Assume that a graphics terminal generates on average 125 byte packets at a rate of 10 packets/sec. A statistical multiplexer is used to connect 25 such graphics terminals to a host. The users require a one way delay of 100ms.

a) Find the capacity that will be required to achieve the stated performance objective.

b) Given the capacity found in part b) find the average number of packets in the statistical multiplexer.

5. Design a statistical multiplexer, i.e., specify the output line rate in b/s and buffer size so the average delay is less than 512 ms and the probability of a blocked packet is less than 2x10-4. The average arrival rate to the multiplexer is 10 packets/second with an average size of 1024 bits. Assume the interarrival and message length p.d.f.'s are exponential.

6.** ** Suppose a future digital video service statistically multiplexes 50 variable bit rate (VBR) video channels onto one fiber. Assume on average the video packets are 2000 bits long and the arrival rate is 1000 packets/sec/channel. The link speed is 150Mb/s.

a) Find the average number of video packets in the system.

b) What is the average delay for the video packets?