3. In an M/M/2 communication node, packets arrive according to a Poisson process of rate 18 packets per second. The system has two parallel crossbar switches, and each switch spends an exponentially distributed amount of time with mean 100 ms to process a packet. (a) Find the probability that an arriving packet must wait to be processed. (b) Find the mean number of packets in the system. (c) Find the mean time a packet spends in the system. (d) Find the probability that more than 50 packets are in the system.

3. In an M/M/2 communication node, packets arrive according to a Poisson process of rate 18 packets per second. The system has two parallel crossbar switches, and each switch spends an exponentially distributed amount of time with mean 100 ms to process a packet. (a) Find the probability that an arriving packet must wait to be processed. (b) Find the mean number of packets in the system. (c) Find the mean time a packet spends in the system. (d) Find the probability that more than 50 packets are in the system.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.10: Exponential Queues In Series And Open Queuing Networks

Problem 8P

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