Consider a router to which packets arrive as a Poisson process at a rate of 4,50

Question

Consider a router to which packets arrive as a Poisson process at a rate of 4,500 packets/sec such that the time taken to service a packet has a Poisson distribution. Suppose that the mean packet length is 250 bytes, and that the output link capacity is 10 Mbps.

a.) What is the mean residence time Tr of a packet in the system?

b.) What is the mean number of packets waiting to be processed in the queue?

Given formulas:

Table 8.4 Notation Used in This Chapter arrival rate, mean number of arrivals per second mean service time for each arrival, amount of time being served, not counting time waiting in the queue standard deviation of service time utilization; fraction of time facility (server or servers) is busy traffic intensity mean number of items in system, waiting and being served number of items in system, waiting and being served mean time an item spends in system (residence time) time an item spends in system (residence time) standard deviation of r standard deviation of 1, mean number of items waiting to be served standard deviation of w mean waiting time (including items that have to wait and items with waiting time = 0) = 7, = = = = = T, TR = = = = = w Tw 7 = Tzmean waiting time for items that have to wait N = number of servers mx(y) = the yth percentile; that value ofy below which x occurs y percent ofthe time

Explanation / Answer

? = 4500 packets/sec

Ts = ( 250

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