Chapter 1b: Circuit Switching

1. ETM 7012 Transmission & Switching: Switching Chapter 1b: Circuit Switching By Bryan Ng bryan@mmu.edu.my

2. Outline • History and Evolution of circuit switching - PSTN • Manual, Strowger, register, cross bar system, trunking, electronic and digital switching systems • Intro to Telecommunication Traffic Engineering • Trunking concept • Congestion • Traffic Model • Loss Call System • Traffic Performance • Loss System in Tandem

3. Public Switched Telephone Network (PSTN) • Public Switched Telephone Network (PSTN) consists of switching nodes (called exhanges) in hierarchical structure: • (a) Local network – connect customers’ stations to LEs • (b) Junction network – interconnect group of LEs • (c) Trunk / toll network – provides long distance circuits within country • (d) International network – provide circuits between countries

4. PSTN- history Before automatic switching exchange was invented, manual crossbar switchboard was used Manual crossbar switchboard Automatic switching exchange Guess what was Mr. Strowger’s job when he invented the automatic switch?

5. Strowger step-by-step system • Strowger invented two-motion selector. E.g. Dialling no. 4388

6. What is a Register? • Receives number dialled by customer and store it for routing decision. • If necessary, part of the number is translated into a different number. • Registers that are added to step-by-step exchanges are called director. • It also functions as a lookup table for routing purpose.

7. Crossbar Switch • G. A. Betulander invented an economic solution in 1917.

8. 2-stage link network using 10x10 switches • Can make more than one connection at a time • Link 23 connects outlet 3 of primary switch 2 to inlet 2 of secondary switch 3

9. Electronic Switching • Electromechanical switches wear out earlier • Electronic device is much more lasting disregard of the frequency of use • Advances in computer technology led to the development of store-program-control (SPC) that offer a wider range of facilities: • Ease customization and modification (electronically) • User control functions such as call barring, repeat last call, reminder call, call diversion, three-way call, charge advise, etc.

10. Digital Switching Systems • Time-division multiplexing (TDM)transmission was initially introduced for trunk and junction circuits in the form of pulse-code modulation (PCM). • If TDM transmission is used with space-division tandem switching, it is necessary to provide demultiplexing of PCM channels to audio signals before switching and multiplexing of audio signals into PCM channels after switching for retransmission.

11. PSTN- a potted history • Digitisation • 1937: Alex Reeves invents PCM • leads to all digital networks (PDH, ISDN)

12. Digital switching systems: audio & PCM mix • Initially, a tandem exchange has mixture of PCM and analog audio junctions. • PCM terminal equipment is needed for audio junctions – audio coding and multiplexing. • The proportion of audio junction has decreased significantly.

13. Digital switching systems: trunk & junction switch • There are no customer lines involved in tandem exchanges – no disadvantage of high-cost customers’ lines. • Thus, digital exchanges were first introduced for trunk and junction switching. • This led to the conversion of trunk networks into integrated digital networks (IDN) – digital transmission and switching.

14. Digital switching systems: local exchange • Digital switching can be applied to local exchange by introducing concentrators • cheap line circuits are retained and large number of subscribers share PCM equipment to access TDM switch. May be used for multiple extension lines or other analog low bandwidth signals.

15. Digital switching systems: local exchange • Figure (c) shows a local exchange with codecs in customer line circuits -> fully digital local exchange.

16. Digital switching systems: local exchange • We can set up digital concentrators at local exchanges and connect them to a TDM route switch at large parent exchange via PCM trunks. • This enables wider coverage area of exchange since PCM trunks are not so much limited by length. • The next evolutionary step is to move PCM codec from exchange end to customer end. • Digital line all the way to customer. This enables data transmission by removing codec. The concept of integrated service digital network (ISDN).

17. Tele-traffic engineering • Introduction • Telephone traffic profile • Definition • Trunking • Congestion • Traffic performance

18. Introduction to Teletraffic Engineering • In the design of a telecommunication system, initial decision must be made regarding its size in order to obtain the desired capacity. • Need to estimate the traffic amount and thus no. of trunks provided. • In teletraffic engineering, trunk any entity that will carry one call. The entity can be international circuit (thousands of km) or wires in between switches (a few metres). • The number of trunks to be provided obviously depends on the traffic to be carried. • It must be sufficient for the busiest time. However, this will results in most equipment idling during non-busy hours.

19. Telephone traffic profile • Operator thus offer cheaper call rates during off-peak hours. It costs them almost nothing to carry such calls. • If they manage to shift some calls from peak to off-peak hours, less equipment and thus capital expenditure are needed. An example of telephone traffic profile of a service area:

20. Traffic • The traffic intensity (sometime referred simply as traffic) is defined as the average number of calls in progress simultaneously during a particular period of time. • It is dimensionless but a name has been given to the unit of traffic : Erlang (E) named after A. K. Erlang, the Danish pioneer in traffic theory. • One Erlang (E) represents the amount of traffic carried by a trunk that is completely occupied i.e. one call-hour per hour or one call-minute per minute. • Traffic Theory • 1915: A. K. Erlang

21. Traffic • The traffic carried by a groups of trunks is A = traffic in Erlangs C = average number of call arrivals during time T h = average call holding time

22. Trunking concept

23. Trunking concept • The concept of trunking allows a large number of users to share the relatively small number of trunks/links by providing access to each user, on demand, from a pool of available trunks/links. • Trunking exploits the statistical behaviour of users so that a fixed number of trunks/links may accommodate a large, random user community. • On a group of trunks, the average number of calls in progress depends on : • The number of calls which arrive • Their duration (holding time)

24. Trunking concept • A single trunk cannot carry more than one call, traffic A for a single trunk is  1. The traffic is a fraction of an Erlang equal to the average proportion of time for which the trunk is busy. This is called the occupancy of the trunk. • The probability of finding a trunk busy is equal to the proportion of time for which the trunk is busy. Thus this probability = occupancy of the trunk.

25. Congestion • It is uneconomic to provide sufficient equipment to carry all the traffics that could possibly offered to a telecommunication system. • In a telephone exchange, it is possible that all subscribers make calls simultaneously. The cost of meeting the demand is prohibitive. • Therefore, there is a possibility that all trunks in a group of trunks are busy  congestion. • There are 2 types of telecommunication system : • Lost Call (LC) system • Delay/queuing system

26. Congestion • In delay systems, calls coming in during congestion wait in a queue until an outgoing trunk becomes free. • In lost call system, the call will be just dropped. • Telephone systems are normally lost call systems. • In such systems, • Traffic carried (Ac) = traffic offered (Ao)- traffic lost (Al) • The proportion of calls that is lost or delayed due to congestion is a measure of the quality of the service provided. It is called grade of service (GOS), B :

27. Congestion • B= proportion of the time for which congestion exists. • = probability of congestion. • = probability that a call will be lost due to congestion. • Thus, if traffic Ao Erlangs is offered to a group of trunks having a GOS, B, the traffic lostisAoB and the traffic carriedis • Ac = Ao(1 - B) • The larger the GOS, the worse is the service given. • If GOS is too large it will results in many users unable to make successful calls and thus dissatisfied. • If GOS is too small, unnecessary expenditure on equipment which is rarely used is made. • In practice, GOS is higher for more expensive trunks.

28. Dimensioning • The basic problem: dimensioning problem i.e. given the offered traffic, A, and the specified GOS, B, find the number of trunks, N, that is required.

29. Traffic model • In order to obtain analytical solutions to teletraffic problems, it is necessary to have a mathematical model of the traffic offered. • A simple model is based on the following assumptions : (1) Pure-chance traffic - call arrivals and terminations are independent random events. (2) Statistical equilibrium - the generation of traffic is a stationary random process i.e. the probabilities do not change during the period considered.

30. Traffic model • The number of call arrival in a given period of time, T has Poisson distribution. • The intervals between callarrivals, T are intervals between two independent events and the distribution is given by a negative exponential distribution • The call duration, H is modelled as a negative exponential distribution • For a group of N trunks the number of calls in progress varies randomly. This is an example of birth and death process or renewal process. • The number of calls in progress (i.e., so called the state) is always between 0 and N. • Such process is called a simple Markov chain. Its behaviour depends on the probability of change from each state to one state before or after the state.

31. Transition probabilities State probabilities Traffic model • Simple Markov chain. • At statistical equilibrium, the probabilities do not change and process becomes regular Markov chain.

32. Lost call systems • Using the traffic model described earlier, Erlang determined the GOS of a loss-call system having N trunks, when offered traffic is A : • The following assumptions are made : (1) Pure-chance traffic (2) Statistical equilibrium (3) Full availability - every call arrives can be connected to any outgoing trunk which is free (4) Calls that encounter congestion are dropped

33. Lost call systems • Erlang found that the probability of x trunks is busy is given by: If call arrivals have Poisson distribution, so does the number of call in progress When N is large, it can be approximated as, given that • The probability of a lost call which is the GOS, B = E1,N(A) = P (N) Erlang lost call formula (or Erlang B) • It can be shown that: The second eqn allows E1,N(A),to be computed for all values of N interactively

34. Lost call systems • A group of five trunks is offered 2E of traffic. Find: • The grade of service • The probability that only one trunk is busy • The probability that only one trunk is free • The probability that at least one trunk is free • Solutions: 1. From Erlang lost call formula 2. From P(1) = 2/7.2667 = 0.275 3) P(4) = (16/24)/7.2667 = 0.0917 4. P(x<5) = 1 – P(5) = 1 – B = 1 – 0.037 = 0.963

35. Lost call systems

36. Traffic performance • If the offered traffic, A increases, the number of trunks, N, must obviously be increased to provide a given GOS. • However, for the same trunk occupancy (or utilization), the probability of finding all trunks busy is less for a large group of trunks than for a small group. • Thus for a given GOS, trunk occupancy is higher in a large group of trunks than a small group  large group is more efficient. • This is the concept of trunking as explained earlier or principle of concentration: it is more efficient to concentrate traffic onto a single large group of trunks.

37. Traffic performance • The penalty paid for high efficiency of large group is that the GOS deteriorates more with traffic overloads compared to small group.

38. Traffic performance

39. Traffic performance • Example : for trunk groups dimensioned to provide GOS of 0.002 at their normal load, a 5-trunk group suffers GOS increase of 40% when traffic overload of 10% occurs while a 100-trunk group suffers a 550% increase in GOS. • Most telecommunications operators adopt dual criteria: two GOSs are specified - one at normal traffic load and another, larger GOS for a given percentage of overload. • The number of trunks provided is determined by which criterion requires the greater number.

40. Traffic performance

41. Loss systems in tandem • Connection between users may span over multiple links in the system. • Thus the GOS for the whole connection needs to be determined. • Lets look at example of two links connection with each link having GOS, B1 and B2. • Traffic offered to second link = A(1 - B1) • Traffic reaching destination = A(1 - B1)(1 - B2) • = A(1 + B1 B2 - B1 - B2)

42. Loss systems in tandem • The overall GOS = B1 + B2 - B1 B2. • If B1, B2 << 1, then B1 B2 is negligible and the overall GOS is B1 + B2. • In general, for an n-link connection, the GOS is

43. Traffic tables • E1,N(A) is suitable for solving problems : given A and N, find B. • However, in network dimensioning the problem is : given A and B, find N. The equation given earlier is not suitable. Calculated values in table can be used.. (slide 22) (next page)

44. Traffic tables

45. References and Links • J. E. Flood, “Chapter 4: Telecommunications traffics,” Telecommunications, Switching, Traffic and Networks, Prentice Hall, ISBN: 0130333093.