Faculty of Computers and Information
Information Technology Department
Wireless & Mobile Networks (IT422) Fourth Year IT
Cellular Network Sheet Answer
1. Using the Erlang B table, approximate the answers to the following. Also in each
case, give a description in words of the general problem being solved. Hint: Straight-
line interpolation is adequate.
a. Given N = 20, A = 10.5, find P.
b. Given N = 20, P = 0.015, find A.
c. Given P = 0.005, A = 6, find N.
2. A telephony connection has a duration of 23 minutes. This is the only connection
made be this caller during the course of an hour. How much is the amount of traffic
in Erlangs of this connection?
3. Calculate the Erlang loads on a system for the following cases:
a. An average call lasts 200 seconds; there are 100 call attempts per minute.
b. There are 400 mobile users in a particular cell. Each user makes a call
attempt every 15 minutes, on the average. Each call lasts an average of 3
minutes.
c. The number of users in b is increased to 500; each user makes a call attempt
every 20 minutes, on the average. Repeat if the average call length doubles to
6 minutes.
4. The maximum calls per hour in one cell equal 4000 and the average call holding
time is 150 seconds. If the blocking probability is 2%, find the offered load and the
carried load. How many channels are required to handle the load?
5. Calculate the traffic intensity for a 10-channel cell with the following traffic over 1
hour:
Channel 1 2 3 4 5 6 7 8 9 10
Number of calls 17 16 14 12 11 10 7 5 3 2
Total occupied
51 47 43 39 34 28 22 15 9 6
time (min)
6. Consider a mobile system supporting 100 channels per cell. A call blocking
probability of 1% is desired. Mobile users typically user their cell phones once per
10 minutes, on the average, their calls lasting an average of 10 minutes. Say the
system is concentrated in an urban area with density of 500 cell phones per km2.
Calculate the required cell radius if a hexagonal topology is assumed. Repeat if the
mobile users “stay on the line” for 4 minutes, on the average. What happens to the
cell size if, in addition, they start using their phones more often?
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, 7. Consider a system with a reuse parameter C = 3. For this system, 330 channels per
cell become available. Assume that the allowable Erlang traffic load is about the
same number. Calculate the allowable cell radius for a suburban region with a
mobile density of 200 mobiles/km2. Repeat for a system with a reuse parameter of 4.
How do these results change for an urban region with a mobile density of 1000
mobiles/km2? In all cases assume a typical user makes a call once per 15 minutes on
the average, the call lasting is on the average 200 sec.
8. Consider a medium-size city; estimate the path loss for a cellular system with the
following properties:
• Carrier frequency = 900 Mhz.
• Height of transmission antenna (base station) = 40m.
• Height of receiving antenna (mobile station) = 5m.
• Propagation distance between the two antennas = 10 km.
Repeat the calculation for suburban and open areas.
9. A cellular system uses FDMA with a spectrum allocation of 12.5 MHz in each
direction, a guard band at the edge of the allocated spectrum of 10 kHz and a
channel bandwidth of 30 kHz. What is the number of available channels?
10. Consider four different cellular systems that share the following characteristics. The
frequency bands are 825 to 845 MHz for mobile unit transmission and 870 to 890
MHz for base station transmission. A duplex circuit consists of one 30 kHz channel
in each direction. The systems are distinguished by the re-use factor, which is 4, 7,
12, and 19 respectively.
a. Suppose that in each of the systems, the cluster of cells (4, 7, 12, 19) is
duplicated 16 times. Find the number of simultaneous communications that
can be supported by each system.
b. Find the number of simultaneous communications that can be supported by a
single cell in each system.
c. What’s the area covered in cells by each system?
d. Suppose the cell size is the same in all four systems and a fixed area of
hundred cells is covered by each system. Find the number of simultaneous
communications that can be supported by each system.
11. Each user generates an average of 0.03 Erlangs of traffic per hour, with a mean An
analog cellular system has a total of 33 MHz of bandwidth and uses two 25 kHz
simplex (one-way) channels to provide full-duplex voice and control channels. What
is the number of channels available per cell for a frequency re-use factor of (1) 4
cells, (2) 7 cells, and (3) 12 cells?
This study source was downloaded
Wireless & Mobile by Networks
100000853497421 from CourseHero.com on 06-26-2023
Prof. Imane Aly 02:44:14
SaroitGMT -05:00
Ismail 2
https://www.coursehero.com/file/9655562/IT422-HOMEWORK-SOLUTION-Cellular-Network-Sheet-FinalAnswers/
Information Technology Department
Wireless & Mobile Networks (IT422) Fourth Year IT
Cellular Network Sheet Answer
1. Using the Erlang B table, approximate the answers to the following. Also in each
case, give a description in words of the general problem being solved. Hint: Straight-
line interpolation is adequate.
a. Given N = 20, A = 10.5, find P.
b. Given N = 20, P = 0.015, find A.
c. Given P = 0.005, A = 6, find N.
2. A telephony connection has a duration of 23 minutes. This is the only connection
made be this caller during the course of an hour. How much is the amount of traffic
in Erlangs of this connection?
3. Calculate the Erlang loads on a system for the following cases:
a. An average call lasts 200 seconds; there are 100 call attempts per minute.
b. There are 400 mobile users in a particular cell. Each user makes a call
attempt every 15 minutes, on the average. Each call lasts an average of 3
minutes.
c. The number of users in b is increased to 500; each user makes a call attempt
every 20 minutes, on the average. Repeat if the average call length doubles to
6 minutes.
4. The maximum calls per hour in one cell equal 4000 and the average call holding
time is 150 seconds. If the blocking probability is 2%, find the offered load and the
carried load. How many channels are required to handle the load?
5. Calculate the traffic intensity for a 10-channel cell with the following traffic over 1
hour:
Channel 1 2 3 4 5 6 7 8 9 10
Number of calls 17 16 14 12 11 10 7 5 3 2
Total occupied
51 47 43 39 34 28 22 15 9 6
time (min)
6. Consider a mobile system supporting 100 channels per cell. A call blocking
probability of 1% is desired. Mobile users typically user their cell phones once per
10 minutes, on the average, their calls lasting an average of 10 minutes. Say the
system is concentrated in an urban area with density of 500 cell phones per km2.
Calculate the required cell radius if a hexagonal topology is assumed. Repeat if the
mobile users “stay on the line” for 4 minutes, on the average. What happens to the
cell size if, in addition, they start using their phones more often?
This study source was downloaded by 100000853497421 from CourseHero.com on 06-26-2023 02:44:14 GMT -05:00
https://www.coursehero.com/file/9655562/IT422-HOMEWORK-SOLUTION-Cellular-Network-Sheet-FinalAnswers/
, 7. Consider a system with a reuse parameter C = 3. For this system, 330 channels per
cell become available. Assume that the allowable Erlang traffic load is about the
same number. Calculate the allowable cell radius for a suburban region with a
mobile density of 200 mobiles/km2. Repeat for a system with a reuse parameter of 4.
How do these results change for an urban region with a mobile density of 1000
mobiles/km2? In all cases assume a typical user makes a call once per 15 minutes on
the average, the call lasting is on the average 200 sec.
8. Consider a medium-size city; estimate the path loss for a cellular system with the
following properties:
• Carrier frequency = 900 Mhz.
• Height of transmission antenna (base station) = 40m.
• Height of receiving antenna (mobile station) = 5m.
• Propagation distance between the two antennas = 10 km.
Repeat the calculation for suburban and open areas.
9. A cellular system uses FDMA with a spectrum allocation of 12.5 MHz in each
direction, a guard band at the edge of the allocated spectrum of 10 kHz and a
channel bandwidth of 30 kHz. What is the number of available channels?
10. Consider four different cellular systems that share the following characteristics. The
frequency bands are 825 to 845 MHz for mobile unit transmission and 870 to 890
MHz for base station transmission. A duplex circuit consists of one 30 kHz channel
in each direction. The systems are distinguished by the re-use factor, which is 4, 7,
12, and 19 respectively.
a. Suppose that in each of the systems, the cluster of cells (4, 7, 12, 19) is
duplicated 16 times. Find the number of simultaneous communications that
can be supported by each system.
b. Find the number of simultaneous communications that can be supported by a
single cell in each system.
c. What’s the area covered in cells by each system?
d. Suppose the cell size is the same in all four systems and a fixed area of
hundred cells is covered by each system. Find the number of simultaneous
communications that can be supported by each system.
11. Each user generates an average of 0.03 Erlangs of traffic per hour, with a mean An
analog cellular system has a total of 33 MHz of bandwidth and uses two 25 kHz
simplex (one-way) channels to provide full-duplex voice and control channels. What
is the number of channels available per cell for a frequency re-use factor of (1) 4
cells, (2) 7 cells, and (3) 12 cells?
This study source was downloaded
Wireless & Mobile by Networks
100000853497421 from CourseHero.com on 06-26-2023
Prof. Imane Aly 02:44:14
SaroitGMT -05:00
Ismail 2
https://www.coursehero.com/file/9655562/IT422-HOMEWORK-SOLUTION-Cellular-Network-Sheet-FinalAnswers/
