T 305 DIGITAL COMMUNICATIONS Statistical multiplexing The figure

T 305: DIGITAL COMMUNICATIONS Statistical multiplexing The figure below shows an example of the statistical multiplexing of four channels. The multiplexer and demultiplexer do not perform any switching in the sense that there is no choice of which output line to take. Packets that arrive on each input channel to the multiplexer are transmitted on the corresponding output channel of the demultiplexer. Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 1

T 305: DIGITAL COMMUNICATIONS Statistical multiplexing The multiplexer stores the incoming packets in a buffer. There are two reasons for this: 1. the multiplexer cannot transmit data exactly as it arrives because the data rates of the input channel and the multiplexed channel are different; 2. And packets may arrive simultaneously on several input channels. The packets are stored with an extra header that contains their input channel number. n The demultiplexer reverses the process and uses the packet header to identify the output channel. n Buffers are required for each output channel because the demultiplexer can, over a short period of time, receive packets at a faster data rate than it can Arab Open University-Lebanon Spring 2009 Tutorial 16 Block IV transmit. n 2

T 305: DIGITAL COMMUNICATIONS Deterministic multiplexing An example of statistical multiplexing is the use of virtual circuits to carry packets between nodes in a packetswitched network. Typically, there can be many virtual circuits allocated to a transmission medium. n For instance, the protocol in a packet-switched public data network (PSPDN) uses 12 -bit addresses and hence identify 4096 channels. n Packets on each channel arrive continuously, with no gaps Next figure shows anone example a deterministic between them; when packetofends, the next begins. multiplexer in which data from four channels is n. The multiplexer transmits the packets at a higher data multiplexed formchannels a single channel. rate than thetoinput such that the four packets, one from each channel, are transmitted within the time it takes to receive one packet. n n Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 3

T 305: DIGITAL COMMUNICATIONS Circuit Switching One of the main advantages of circuit switching is that the only delay in transferring data is caused by the time necessary to propagate the data through the node. n. Voice communication requires a short propagation delay and cannot tolerate any significant variation. n This makes circuit switching a natural choice for voice traffic. n. One of the main disadvantages of circuit switching is that transmission capacity is reserved for a connection even when no data is transmitted. n. For instance, in a telephone call, normally one person is talking at a time, so at least 50% of the bi-directional transmission capacity for a connection is wasted. n Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 4

T 305: DIGITAL COMMUNICATIONS Switching structures It is important to bear in mind that the data is transmitted as a stream of octets and that the octets are transmitted every 125 μs. This means that a constant data rate of 64 kbit/s is reserved for each direction of transmission for each telephony data channel. n. The operation of a central switching node can be visualized as an array of cross-points that connect input lines to output lines with a dedicated cross-point for each combination of two lines. n. The cross-points represent which input and output lines can be connected and the number of ways in which a connection can be achieved. n. In next figure, each of the five input lines can be connected to any of the five output lines and there is only one path possible through the structure for each connection. n. This size of switch is expressed as a 5 × 5 switching array. n Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 5

T 305: DIGITAL COMMUNICATIONS Switching structures Next figure represents a single-stage switch which connects an input line to an output line using a single cross-point. Because each cross-point is used for only one combination of input line and output line, no existing connection can prevent a connection to a free output line from being set up and we say that the switching unit is non-blocking. n. Blocking occurs in a circuit switch when it is unable to set up a path to a free output line. In a single-stage switching unit the number of cross-points increases rapidly as the number of lines increases. This is important because the number of cross-points that is required in a switching unit strongly affects the size and cost of a node. n Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 6

T 305: DIGITAL COMMUNICATIONS Switching structures A method of reducing the number of the cross-points is to distribute the switching over several stages. Each switching stage consists of several smaller switching arrays. Figure below illustrates a three-stage switching configuration in which N input and output lines are split into m groups of n lines, where n divides exactly m times into N. n. The first stage contains m arrays. Each array switches n input lines to a number of output lines, say k, and each line from a firststage array goes to a different second-stage array. n. This means that in the second stage there are k arrays and each one has m input lines (one for each array in the first stage). n. The third stage, like the first, divides the N output lines into m groups of n lines. Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 7

T 305: DIGITAL COMMUNICATIONS Switching structures Each of the m third-stage arrays has an input line connected to a different second-stage array, so there must be k third-stage input lines and m second-stage output lines. n. A connection is set up between an input line and an output line by operating a cross-point in each of the three stages. n. The first stage connects the input line to a secondstage array which can switch the line to the third-stage array with the required output line. n. The total number of cross-points in the three-stage switching unit is equal to the total number of crosspoints in the first stage plus the number in the second stage plus the number in the third. n Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 8

T 305: DIGITAL COMMUNICATIONS Switching structures The number of cross-points in each switching array in the first stage is n × k and, since there are m arrays, the total number of cross-points in the first stage is m × n × k. Because m × n is the total number of input lines, N, the number of cross-points can be written as N × k. The third stage is the mirror image of the first, so this too has N × k cross-points. The number of cross-points in the second stage is k × m, where k is the number of second-stage arrays. Since each input line to a second-stage array comes from a different array in the first stage, the value of m is equal to the number of first-stage arrays, which is N/n. The total number of cross-points in the second stage can therefore be written as k × (N/n)2. The total number of cross-points in the three-stage switching configuration, N 3, is: n Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 9

T 305: DIGITAL COMMUNICATIONS Switching structures The previous equation shows that if k increases so does the number of cross-points, and if n increases the number of cross-points decreases. Therefore, to minimize the number of cross-points, maximize the value of n and minimize the value of k. n n Next figure shows an example of a three-stage switching configuration for 16 input lines that is blocking. There are four first-stage arrays (m = 4), each with four input lines (n = 4), and there are five second-stage arrays (k = 5). Using above equation, the total number of cross-points in the 16 × 16 three-stage configuration is: Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 10

T 305: DIGITAL COMMUNICATIONS Switching structures Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 11

T 305: DIGITAL COMMUNICATIONS Switching structures n. In previous figure, five paths are set up. n. These are: n❚ from input line 0 to output line 15 using second-stage array 4 n❚ from input line 2 to output line 11 using second-stage array 2 n❚ from input line 3 to output line 0 using second-stage array 1 n❚ from input line 4 to output line 6 using second-stage array 0 n❚ from input line 6 to output line 4 using second-stage array 3. n. Suppose a path between input line 1 and output line 7 needs to be set up. n. Since the output line is free, if the switching configuration is nonblocking then a path could be found. However, the only second-stage arrays available to first-stage array 0, which has input line 1 connected to it, are 0 and 3. n Both these second-stage arrays use their line to third-stage array 1 for other paths, and so are not available to set up a path to output line 7. The three-stage switching configuration can be made non-blocking by increasing the value of k. The non-blocking condition for a three-stage switching configuration is: Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 12

T 305: DIGITAL COMMUNICATIONS Digital space switching Two types of cross-point used in digital circuit-switched nodes are: digital space switching and digital time switching. The terms ‘space’ and ‘time’ are used to describe how the paths through the switching configurations are separated. n n The first automatic telephone exchanges used space switching in which the paths were set up using electromagnetic devices such as that shown below. n. The physical separation between paths in these devices was quite large but the present day versions of digital space switching in telephone exchanges use integrated circuits in which the physical separation between paths is in the order of microns, or smaller. Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 13

T 305: DIGITAL COMMUNICATIONS Digital space switching transfers digital signals from one input line to an output line. Figure below shows an example of a 2 × 2 space switch, where the input and output lines carry digital signals, but the data is not multiplexed and only one channel uses each line. The data carried by the signals is represented as rectangles above the input and output lines in the figure. Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 14

T 305: DIGITAL COMMUNICATIONS Digital space switching Figure below represents a digital space switch connecting two TDM signals, each with four time slots, labeled 0, 1, 2 and 3. n Fig. Multipl exer (data select or). n Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 15

T 305: DIGITAL COMMUNICATIONS Digital space switching Next figure shows the same time-multiplexed space switch as previous one but uses multiplexers as columns of space switches. In this case the multiplexers have only two input lines instead of four, so only one selection line is required to specify which input line is used. The cross-points in each multiplexer are controlled by a connection store containing the input number that is operated for each time slot in a TDM frame. Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 16

T 305: DIGITAL COMMUNICATIONS Packet Switching n Packet-switching exchanges (PSEs) have used the concept of stored program control (SPC) since the first generation of exchanges, in the late 1960 s, which were general-purpose computers that moved packets from an input queue to an output queue. n. Later, front-end processors were added to perform low-level functions such as error control at the data link level. n. Figure below illustrates the structure of the first generation of PSEs. n All the data switched by a PSE went via the central processor, which also had other tasks to perform. n. Packets were transferred to input buffers where they waited for the central processor to analyze their Arab Open University-Lebanon contents. Spring 2009 Tutorial 16 Block IV 17

T 305: DIGITAL COMMUNICATIONS Banyan Network Example Step 1 Required output location. Specified in the Packet header. This example says it needs to be switched to out put six (110) Looks at most significant bit & switches to that value at the output Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 18

T 305: DIGITAL COMMUNICATIONS Step 2 Spring 2009 Now it looks at the middle bit to switch the output Arab Open University-Lebanon Tutorial 16 Block IV 19

T 305: DIGITAL COMMUNICATIONS Step 3 Spring 2009 Finally, the least significant bit examines the output required Arab Open University-Lebanon Tutorial 16 Block IV 20

T 305: DIGITAL COMMUNICATIONS A method of overcoming the problem of internal link blocking in a banyan network without using buffers is to arrange that, in a switching cycle, the packets appear on the input lines in such a way that their paths through the banyan network do not conflict. This can be achieved in two stages. The first stage is to use a sorting network to switch the packets so that they appear in ascending address order at the output lines of the sorting network. The second stage is to distribute (or shuffle) the output lines of the sorting network over the Arab Open University-Lebanon input lines of the internal link blocking Spring 2009 banyan network to avoid Tutorial 16 Block IV 21

T 305: DIGITAL COMMUNICATIONS Example: Batcher sorting network Spring 2009 Arab Open University-Lebanon Tutorial 16 Block IV 22