Solutions to Chapter 4 - Communication Networks

Communication Networks (2 nd Edition)
Chapter 4 Solutions
7 9 0.362 7 90 0.923
8 9 0.289 . . .
9 9 0.224 . . .
10 9 0.168 100 90 0.027
As shown, a lower probability of blocking is achieved by scaling up the system.
59. Calls arrive to a pool of 50 modems according to a Poisson process. Calls have an average
duration of 25 minutes.
Solutions follow questions:
a. What is the probability an arriving calls finds all modems busy if the arrival rate is two calls
per minute
For this system, the utilization a = 2/(1/25) = 50 and c = 50. The probability of blocking is:
P b =
c
a
c!
c
a
j
j
j=
0 !
= 0.105
b. What is the maximum arrival rate that can be handled if the maximum acceptable blocking
probability if 1% 10%
If the maximum acceptable blocking probability is 10% and 1%, the maximum handled arrival
rates, given a service rate of 1/25 calls per minute are:
P b Load
1% 1.516 calls/minute
10% 1.982 calls/minute
60. Consider dynamic nonhierarchical routing (DNHR).
Solutions follow questions:
a. Explain how DNHR can be used to exploit the time differences between different time zones
in a continent.
In the morning in the east, the business day begins and long-distance calls are made between
cities on the East Coast. The west-coast business day has not yet begun, so the links from east
to west are relatively under-utilized.
Eastern traffic can be re-routed through the western free lines to provide additional capacity for
the traffic between eastern cities. The opposite can occur in the evening after the business day in
the east ends and the under-utilized eastern trunks are used for western traffic.
b. Explain how DNHR can be used to exploit different business and residential activity patterns
during the day.
For local calls during business hours, traffic may be re-routed through relatively non-busy lines in
residential area to free up resources in the business areas. The opposite can be done in the
evening when most people are in the residential areas and the telephone traffic in the business
area is low volume.
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