hw3 - are identically and exponentially distributed with...

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ECE 547: Homework 3 Due: Oct. 7, 2008 1. A telephone company establishes a direct connection between two cities expecting Poisson traffic with rate 30 calls/min. The durations of calls are independent and exponentially distributed with mean 3 min. Interarrival times are independent of call durations. How many circuits should the company provide to ensure that an attempted call is blocked (because all circuits are busy) with probability less than 0.01? It is assumed that blocked calls are lost (i.e., a blocked call is not attempted again). 2. An internet access point A receives two packet streams (possibly with different quality-of- service requirements), and transmits them on a first-come first-serve basis using a common internet connection with capacity C . The two input streams are assumed to be independent Poisson processes, and their rates are λ 1 and λ 2 , respectively. In addition, their packet lengths
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Unformatted text preview: are identically and exponentially distributed with mean L . The internet access point A is assumed to have in²nite bu±ers. However, packets From two streams are treated di±erently. A packet From stream 1 is always accepted by A . A packet From stream 2 is accepted only iF the number oF packets in A (including the packet under service) is less than or equal to a number K > 0; otherwise, it is assumed lost. (a) Derive P n , the steady-state probability that there are n packets in the access point A . (b) ³ind the rate with which packets From stream 2 are lost. (c) ³ind the expected delay From the time a packet From stream 1 arrives at the access point A to the time when it completes service. (d) ³ind the expected number oF packets From stream 1 that are in the access point A . 3. Solve problems 2-9, 2-11, 2-13, and 2-20 in the Schwartz book....
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