Subject Name Digital Switching Systems Subject Code 10

Subject Name: Digital Switching Systems Subject Code: 10 EC 82 Prepared By: Aparna. P, Farha Kowser Department: Electronics and Communication Date: 3 -3 -2015 2/25/2021

Unit 3 Telecommunication Traffic

• • Unit of traffic Congestion Traffic measurement GOS Mathematical Model of traffic Lost call systems Queueing systems

TRAFFIC DESIGN REQUIREMENTS • In the study of tele traffic engineering, to model a system and to analyze the change in traffic after designing, the static characteristics of an exchange should be studied. The incoming traffic undergoes variations in many ways. • The traffic is unpredictable and random in nature. So, the traffic pattern/characteristics of an exchange should be analyzed for the system design. The grade of service and the blocking probability are also important parameters for the traffic study.

Traffic Statistics • The following statistical information provides answer for the requirement of trunk circuits for a given volume of offered traffic and grade of service to interconnect the end offices. The statistical descriptions of a traffic is important for the analysis and design of any switching network. • Calling rate • Holding time • Distribution of destinations. • User behavior • Average occupancy

Traffic Pattern • An understanding of the nature of telephone traffic and its distribution with respect to time (traffic load) which is normally 24 hours is essential. It helps in determining the amount of lines required to serve the subscriber needs. • The variations are not uniform and varies season to season, month to month, day to day and hour to hour. • Busy hour. Traditionally, a telecommunication facility is engineered on the intensity • of traffic during the busy hour in the busy session. • Taking into account the fluctuations in traffic, CCITT in its recommendations E. 600 defined the busy hour as follows.

• Busy hour. Continuous 60 minutes interval for which the traffic volume or the number of call attempts is greatest. • Peak busy hour. It is the busy hour each day varies from day to day, over a number of days. • Time consistent busy hour. The 1 hour period starting at the same time each day for which the average traffic volume or the number of call attempts is greatest over the days under consideration.

Call completion rate (CCR). Based on the status of the called subscriber or the design of switching system the call attempted may be successful or not. The call completion rate is defined as the ratio of the number of successful calls to the number of call attempts. Busy hour call attempts Busy hour calling rate. Day-to-day hour traffic ratio

Units of Telephone Traffic • Traffic intensity is measured in two ways. They are (a) Erlangs and (b) Cent call seconds (CCS). • Erlangs. The international unit of traffic is the Erlangs. It is named after the Danish • Mathematician, Agner Krarup Erlang, who laid the foundation to traffic theory in the work he did for the copenhagen telephone company starting 1908.

• Grade of Service (GOS) • For non-blocking service of an exchange, it is necessary to provide as many lines as there are subscribers. But it is not economical. So, some calls have to be rejected and retried when the lines are being used by other subscribers. • The grade of service refers to the proportion of unsuccessful calls relative to the total number of calls. GOS is defined as the ratio of lost traffic to offered traffic.

Blocking Probability and Congestion • The value of the blocking probability is one aspect of the telephone company’s grade of service. • Based on the number of rejected calls, GOS is calculated, whereas by observing the busy servers in the switching system, blocking probability will be calculated. • When the number of sources is large, the probability of a new call arising is independent of the number already in progress and therefore the call congestion is equal to time congestion.

MODELLING OF TRAFFIC • To analyze the statistical characteristics of a switching system, traffic flow and service time, it is necessary to have a mathematical model of the traffic offered to telecommunication systems. • The facilities of the switching systems are shared by many users. This arrangement may introduce the possibility of call setup inability due to lack of available facilities. • The mathematical description of the queueing system characterics is called a queueing model.

Lost Calls Cleared (LCC) System • The LCC model assumes that, the subscriber who does not avail the service, hangs up the call, and tries later. • The first person to account fully and accurately for the effect of cleared calls in the calculation of blocking probabilities was A. K. Erlang in 1917. • The Erlang loss system can be modeled by birth and death process with birth and death rate as follows.

Queueing Systems • In this the call will not lost it will be delayed • The assumptions are § Pure chance traffic § Statistical Equilibrium § Full availability § Calls which encounter congestion enter into a queue and stored until a server becomes free.

Queueing Systems • Second Erlang’s Distribution Let x be the no. of calls in the System. When x<N , then x calls are being served and there is no delay. When x>N, all the servers are busy and incoming calls encounter delay; there are N calls Served and x-N calls in the queue. IF x≤N: There is no queue the system will act as lost call system in the absence of congestion.

Queueing Systems • If x>N: The probability of a call arrival during time δt is given by The Probability of a transition from x-1 to x is given by The probability of call ending is given by The transition probability from x to x-1 is given by

Queueing Systems

Queueing Systems If there is no limit for the queue x can have any value between 0 and ∞ We can write This is second erlangs Distribution formula

Queueing Systems • Probability of Delay. • Delay occurs if all servers are busy, the probability that there at least Z calls in the system is given by

Queueing Systems This is called Erlang’s delay formula