Consider a configuration in which packets are sent from computers on a
LAN to systems on other networks. All of these packets must pass
through a router that connects the LAN to a wide area network and
hence to the outside world (assume that the buffer of the router is
infinite). Let us assume that
packets arrive to the router according to Poisson process with mean
arrival rate of eight packets per second.The average packet length is
144 bytes and is assumed to be exponentially distributed.
a) The line speed from the router to the wide area network is 14400
bits per second. What is the mean
queueing (waiting) time in the router? How many packets are in the
buffer of the router? What is the total
mean time that a packet spends in the router (waiting and
transmission)? What is the average number of
packets in the system?
b) Now assume that the network administrator decides to replace the
line from the router to the wide area
network with a faster one in order to improve the performance of the
system. Please provide the minimum
required line speed in order to meet the following design objective:
the average total time that a packet
spends in the system is less than or equal 0.15 seconds. What is the
average number of packets in the system
in this case?