Wireless & Mobile Systems: Cell Capacity Calculation

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Questions and Answers

What is the formula for calculating the offered load (a) in a wireless system?

a = Arrival Rate / Service Rate

a = Arrival Rate - Service Rate

a = Arrival Rate * Service Rate (correct)

a = Arrival Rate + Service Rate

In a cell with 100 MSs, if 30 requests are generated during an hour with an average holding time T=360 seconds, what is the offered load in Erlangs?

15 Erlangs

10 Erlangs

5 Erlangs

3 Erlangs (correct)

Which queuing model is used to analyze a system with interarrival time of users, distribution of service time, number of channels, and maximum number of users in the system?

M/G/2/3

G/M/2/2

M/M/1/1

M/M/S/S (correct)

What does the Erlang unit represent in the context of wireless systems?

Duration of a call Signup and view all the answers

If the average arrival rate during a short interval t is denoted by 𝜆𝑡, what does 𝜆 represent?

Rate of interarrival time Signup and view all the answers

What does P(i) represent in the M/M/S/S queuing model steady state probability formula?

(i-1)th state probability Signup and view all the answers

What is the blocking probability B(2,3) based on the Erlang B formula?

0.529 Signup and view all the answers

For S=5 and a=3, what is the Erlang C value C(5,3) based on the given formulas?

0.2360 Signup and view all the answers

What does the Erlang B formula represent in terms of call processing?

Blocking probability Signup and view all the answers

In Erlang systems, what does the Erlang C formula determine?

Probability of an arriving call being delayed Signup and view all the answers

How is the efficiency of a system calculated based on the provided formulas?

(aS(S-1)!)/(S-a) + ∑((S-1)!/(S-a)i) Signup and view all the answers

What is the probability of an arriving call being blocked according to the Erlang B formula?

(aS) / S∑k / k! Signup and view all the answers

What is the formula for the Handoff Rate in a Rectangular Area mentioned in the text?

2A(N1cosq + N2sinq)(N1sinq + N2cosq) Signup and view all the answers

How is H minimized in terms of the offered load and cell capacity?

R1N1 = R2N2 Signup and view all the answers

What does the formula 2A(N1cosq + N2sinq)(N1sinq + N2cosq) represent in the handoff rate calculation?

Offered Load Signup and view all the answers

In the context of the text, what does R1 and R2 represent in the handoff rate calculation formula?

Cell boundaries for a rectangular area Signup and view all the answers

How does the differentiation of lH with respect to R1 contribute to minimizing H?

By balancing the total number of MSs per unit length Signup and view all the answers

What is the significance of A in the handoff rate calculation for a rectangular area?

Signifies a fixed area Signup and view all the answers

Study Notes

Wireless System Formulas

The formula for calculating the offered load (a) in a wireless system is not explicitly stated, but it can be calculated using the number of requests, average holding time, and other system parameters.

Offered Load Calculation

In a cell with 100 MSs, if 30 requests are generated during an hour with an average holding time T=360 seconds, the offered load in Erlangs can be calculated.

Queuing Models

The queuing model used to analyze a system with interarrival time of users, distribution of service time, number of channels, and maximum number of users in the system is not specified, but it is likely an M/M/S/S queuing model.

Erlang Units

The Erlang unit represents the measure of the offered load in a wireless system, which is a dimensionless unit.

Queuing Model Parameters

𝜆 represents the average arrival rate in a queuing model.
P(i) represents the steady-state probability in the M/M/S/S queuing model formula.

Erlang Formulas

The Erlang B formula represents the blocking probability of a system, which is the probability of an arriving call being blocked.
The Erlang C formula determines the probability of delay in a system.
The Erlang B formula for blocking probability B(2,3) can be calculated using the offered load and number of channels.
The Erlang C value C(5,3) can be calculated using the offered load and number of channels.

System Efficiency

The efficiency of a system can be calculated based on the blocking probability and other performance metrics.

Handoff Rate

The formula for the Handoff Rate in a Rectangular Area is not explicitly stated, but it involves the offered load, cell capacity, and geometric parameters of the area.
H can be minimized by optimizing the offered load and cell capacity.
The formula 2A(N1cosq + N2sinq)(N1sinq + N2cosq) represents a term in the handoff rate calculation formula.
R1 and R2 represent the lengths of the sides of the rectangular area in the handoff rate calculation formula.
The differentiation of lH with respect to R1 contributes to minimizing H by finding the optimal values of R1.
A is a parameter in the handoff rate calculation formula, which represents the area of the rectangular region.

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Description

Learn how to calculate the cell capacity in wireless and mobile systems based on the average number of mobile stations (MSs) requesting service and the average holding time. Explore how the offered load is calculated using the arrival rate and holding time in a given cell scenario.