Tele Traffic lecture

8/12/2019 Tele Traffic lecture

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Teletraffic Engineering

January 2013

Teletraffic Engineering January 2013 1 / 18
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Traffic Engineering

Traffic engineering uses statistical techniques such as queuing theoryto predict and engineerthe behavior of telecommunications networkssuch as telephone networks or the Internet.

One of the important steps of teletraffic engineering determines numberof channels required on a route or a connection between two MSCs1.Another important steps of teletraffic engineering is to ensure thedesired

1Mobile switching centre server which is a 3G termTeletraffic Engineering January 2013 2 / 18
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Busy hour

Busy hour - uninterrupted period 60 min during which the trafficvolume is highestUsed for traffic dimensioningCan be: fixed/mobileIn heterogeneous networks busy hours for different traffic types maynot coincide

In cellular network, busy hour occurs at different time for differentcells

Figure : Typical daily traffic usage in acellular system.Teletraffic Engineering January 2013 3 / 18
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Service Level

Service Level can be divided into two main areas:

1 Dial tone delay: The maximum waiting time to hear a dial toneafter removing the hand-set from the hook.

2 Service blocking probability:the probability that service delay will exceed some specific value or

The probability that the call will be denied or blocked

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Service or call blocking probability is known as the grade of service(GoS)

GoS= Block CallTotal Call

(1)

GoS= Block Call

Serviced calls+Blocked calls =

10

380 + 10=

1

39 (2)

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Basic Queueing Theory

Figure : Number of customers as a function of time

(t): Number of customers who have come to the system and not rejected in theinterval (0, t)(t): Number of customers who have left the system and completed served in (0,t)N(t): (t) (t) Number of customers in system at time t(t): Total time that all customers together have spent in the system during the

intervalTeletraffic Engineering January 2013 6 / 18
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Basic Queueing Theory - Birth-Death Processes

A Birth-Death is a special type of discrete-time or continuous time MarkovChain with the restriction that at each step, the state transitions, if any,can occur only between neighbouring states.

The underlying Markov process representing the number of customers insuch systems is know as a birth-and-death process. The birth-deathterminology is used to represent increases and decreases in the populationsize. The corresponding events in queueing systems are arrivals and

departures.

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Again using the birth (arrival)-death (departure) terminology, when the

population size is n, let n and n be the infinitesimal transition rates(generators) of birth and death, respectively.

When the population is the number of customers in the system, n andnindicate that the arrival and service rates depend on the number in the

system.

If the process is a Birth-death process and if the current state Xn is i, thenthe above condition implies that the next state Xn+1 can only be i-1, i ori+1.

Based on the properties of the Poisson process, i.e., when arrivals are in aPoisson process and service times are exponential, we can make thefollowing probability statements for a transition during (t, t + t]:

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birth(n 0):

P(one birth) = nt + o(t)P(no birth) = 1 - nt + o(t)

P(more than one birth) = o(t)death(n > 0):

P(one death) = nt + o(t)

P(no death) = 1 - nt + o(t)P(more than one death) = o(t)

where o(t) is such that o(t)t n 0 as t0. Since a continouse-timeprocess is being considerd, we need to focus on changes in the process

over time interval o(t) as o(t) 0. Let kbe the birth rate in statek2 Similarly, let kbe the death rate in state k.

2Note that is these statements the o(t) terms do not specify actual values. In eachof the two cases, the o(t) terms sum to 0 so that the total probability of the three

events is equal 1.Teletraffic Engineering January 2013 9 / 18
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Figure : State Transition Diagram (Birth-Death)

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Basic Queueing Theory - Another Way

Let Q(t) be the number of customers in the system at time t. Define

Pik(t) =P[Q(t) =k|Q(0) =i]Considering transitions over a time interval t as t 0 , we get that

P{state k to state k+1 in time t} = Pk,k+1 =k(t)P{state k to state k-1 in time t} = Pk,k1 =k(t)

P{state k to state k in time t} = Pk,k= 1 (k+k)(t)P{other transitions in t} = 0

Considering the transitions of the process Q(t) for the state transitionsbetween the time instant tand the time instant t+ twe have (in otherwords (t, t+ t]) we have

P0(t+ t) = P0(t)[1 0t] +P1(t)1t

Pk(t+ t) = Pk(t)[1 (k k)t] +Pk1(t)k1t+Pk+1(t)k1t

with

k=0Pk(t) = 1Teletraffic Engineering January 2013 13 / 18
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Figure : State Transition Diagram (Birth-Death)

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ErlangB Formula

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C i f C ll


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Capacity of a Cell

This is Erlang B formula B(C, A)

In the previous example, if C = 2 and A = 3, the blocking probabilityB(2, 3) is

B[2, 3] = AC/C!

C

i=0Ai

i!

= 32/2!

2i=0

3i

i!

= 0.529

So, the number of calls blocked 30 0.529 = 15.87

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Tele Traffic lecture

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