Exercise 5: Erlang Delay Systems
1
Erlang Delay System compared to Erlang Loss
System
Consider two dierent systems. One system is an M/M/k/k system and the other is
an M/M/k.
a) The Erlang Loss or the Erlang-B formula is given by:
Ek (A) =
Ak /k!
k
v=0
Av
NTNU
Norwegian University of Science and Technology
Department of Telematics
TTM4155
Teletraffic Theory
Formula Collection
31.08.09
Permitted as a help aid during the examination, without the additional
information.
General Notation
, : intensities
A: O
1
Erlang Loss Systems
1.1
Multiple Classes
Consider a system with three classes of customers. Class i customers arrive at rate of
i , i = 1, 2, 3, each of which requires exponentially distributed service with parameter
i , i = 1, 2, 3. There are k servers
Exercise 3: General Queuing
Concepts and M/M/1 system
1
PASTA
Consider a D/D/1 system. The system is empty at time 0 and then there are arrivals
every two time slots, at time slots 1,3,5.The service time is 1.
a) Does this system have the PASTA property?
Markov Chains
1
Discrete or Continuous Markov Chain
What is the dierence between a continuous time Markov Chain and a discrete Markov
Chain?
2
Two state Markov Chain
Consider a communications system which transmits digits 0 and 1. Each digit transmitted m
Exercise 3: General Queuing
Concepts and M/M/1 system
1
PASTA
Consider a D/D/1 system. The system is empty at time 0 and then there are arrivals
every two time slots, at time slots 1,3,5.The service time is 1.
a) Does this system have the PASTA property?
Exercise 0.1 Do you remember TTM4110?
This exercise is composed of questions taken from multiple choice tests (selftests) given in the course TTM4110
(Dependability and Performance with Discrete Event Simulation) which is a recommended background for this
Exercise 0.1 Do you remember TTM4110?
This exercise is composed of questions taken from multiple choice tests (selftests) given in the course TTM4110
(Dependability and Performance with Discrete Event Simulation) which is a recommended background for this
Exercise 4: Loss Systems
September 16, 2009
1
Multiple Classes and Erlang Loss
Consider a system with three classes of customers. Class i customers arrive at rate of
i , i = 1, 2, 3, each of which requires exponentially distributed service with parameter
Exercise 3
Transforms
1.
1
Transforms
1.1
Merging Poisson Streams
Two arrival streams from Poisson sources are merged. The arrival rates are 1 and 2 , see fig.
Two arrival
1. see g. 1 streams from Poisson sources are merged. The arrival rates are 1 and 2
Exercise 5: Erlang Delay Systems
1
Erlang Delay System compared to Erlang Loss
System
Consider two dierent systems. One system is an M/M/k/k system and the other is
an M/M/k.
a) The Erlang Loss or the Erlang-B formula is given by:
Ak /k!
Ek (A) =
k
v=0
Av
Markov Chains
1
Discrete or Continuous Markov Chain
What is the dierence between a continuous time Markov Chain and a discrete Markov
Chain?
See Ex Moshe Zukerman or Google for more detail.
2
Two state Markov Chain
Consider a communications system which t
An Internet Trac Study
Semester Assignment
TTM 4155: Teletrac Theory
Fall 2009
1
Assignment Requirement
The assignment is mandatory for students who register for TTM 4155: Teletrac Theory. The assignment should be carried out in group of two students. Eac
Exercise 3
N
Given P n = ( N = n ) and P ( z ) = E ( z )
Let q j = P ( N > j )
qj z
Find Q ( z ) =
j
Transforms
j=0
4.
1
1.
Given F ( z ) =
1.1
Transforms
i
z
- fi z = Poisson( 1 2z Merging ( 1 z )2 Streams
)
i=0
Two arrival streams from Poisson sources