Question

PROBLEMS 591 8.2 A link with transmission rate R1 Mbi/s is used to forward packets having random size e, which is assumed to be uniformly distributed in the discrete set L [1,2,..., 100] kbyte. a) Find the mean transmission time my of a packet along the line. b) Find the probability that the transmission time of a packet is larger than 500 ms. 8.3 A link with transmission rate R, is used to forward packets having random size E, which is assumed to have geometric PMD Prove that, if m 1/p is large enough, the distribution of the packet transmission times can be approximated to an exponential distribution with parameter pRme 8.4 A dentist clinic opens up for business at 0.Customers arrive according to a Poisson rp with rate 2. Each medical treatment takes a random time y. Find the probability P that the second arriving customer will not have to wait and the average value my of his waiting time for the two following cases: a) y c-constant. b) y is exponentially distributed with parameter 1/c Little's Law 8.5 A hotel clerk takes, on average, my-3 min to attend to a single customer. Assuming that customers arrive at the clerk desk with average rate of ?-, 0.1 customer/min, determine the period of time the clerk is idle. 8.6 Consider a transmission system where the packet transmission along the line takes a random time, with uniform distribution in the interval [1, 1000] pus. Knowing, that the mean waiting time in a queue is my 500 us and that, on average, there are ma 0.2 packets in the waiting buffer, determine: a) The mean number of packets in the system. b) The period of time the line is engaged. A router is busy processing data packets for 80% of the time. On average mg-32 packets are waiting for service. Find the mean waiting time m processing time is my 1 s. of a packet given that the mean

Answer 1

ANSWER:

FOR 1:

utilization =Transmission time/ transmission time+rtt

Mean transmission time=length of packet/bandwidth

=1kb/1mbps

= 1*10^3*8/1*10^6

=8 Ms of a packet along the line

FOR 2:

Probability that the transmission time of the packet is following

Probability = 8/8+500

=0. 0157