1. T305: DIGITAL COMMUNICATIONS Arab Open University-Lebanon Tutorial 181 T305: Digital Communications Block 4 – Modelling Activities: Traffic

2. T305: DIGITAL COMMUNICATIONS 2 Arab Open University-Lebanon Tutorial 18 Questions 1-What is main advantage of using the flooding protocol? routeing tables can be avoided by using very simple strategies. 2- Explain the meaning of the Bellman-Ford algorithm: D ij (h+1)=min K [d ik+ D kj (h)]. K is a neighboring node to i and i±j. The algorithm takes the minimum of all possible paths between the source node, I and a specific destination j, using any directly connected node (neighboring) node, k.

3. T305: DIGITAL COMMUNICATIONS 3 Arab Open University-Lebanon Tutorial 18 Questions 3- Define circuit swithcing. A circuit-switched network is one that sets up a physical circuit end-to-end for the exclusive(الحصري) and continuous transfer. 4- Why t ransmission capacity is used more efficiently( بكفاءة ) in packet-switched networks than in circuit-switched networks? In a packet-switched network, transmission capacity is used only when a packet is actually being transferred

4. T305: DIGITAL COMMUNICATIONS 4 Arab Open University-Lebanon Tutorial 18 Questions 5- What is difference in term of the transmission capacity between deterministic multiplexing and statistical multiplexing? In case of statistical multiplexing the sum of the maximum data rates achievable by all of the (input) data channels that can use the transmission medium can exceed the maximum capacity of the (ouput) transmission medium. While in the case of deterministic multiplexing they are equal. 6- State the non-blocking condition for a three-stage switching configuration is:

5. T305: DIGITAL COMMUNICATIONS 5 Arab Open University-Lebanon Tutorial 18 Plan Traffic Topic 1: Introduction Topic 2: Specification Of Queues(قوائم الانتظار) Topic 3: Quantifying(الكمي) Traffic(حركة المرور) Topic 4: Multiple-Server Queues Preparation for Next Tutorial

6. T305: DIGITAL COMMUNICATIONS 6 Arab Open University-Lebanon Tutorial 18 Topic 1: Introduction: Terminology:( مصطلحات )  Buffer: memory element to store data used for a particular Job.  Job: task that needs to be carried out, e.g. checking packet headers for errors.  Servers: processing elements, hardware or software, depending on the Job processing involved.  Queuing system: combination of buffer and servers.  Network congestion:In any network when there is too much the data traffic at a node that the network slows down or starts loosing data, it is known as network congestion. It degrades quality of service and also can lead to delays, lost data. ServerBuffer ArrivalsDepartures

7. T305: DIGITAL COMMUNICATIONS 7 Arab Open University-Lebanon Tutorial 18 Introduction: Queuing System ( نظام الطابور )  Target:(الهدف)  Meet specified cost constraints(مواجهة قيود التكاليف المحدودة)  Meet quality of service (QoS) requirements, e.g.  maximum processing delay for jobs  maximum number of packets rejected (buffer full) the storage capacity of the buffer need to be chosen so as to allow the system to meet its specified cost constraints and quality of service requirements, such as maximum processing delay for jobs, or maximum number of packets rejected because the buffer was full when the job arrived.  Strategy:(تخطيط)  Select number of processing elements (servers)  Select storage capacity of the buffer

8. T305: DIGITAL COMMUNICATIONS 8 Arab Open University-Lebanon Tutorial 18 Introduction: Queuing System  Design Queuing System or evaluate its Performance:(الأداء)  Know nature of demand placed(وضع الطلب) upon them  Know Peak(قمة) Demand in particular In order to design or evaluate the performance of queuing systems, it is necessary to know the nature of the demand placed upon them and, in particular, the peak demand.  Demand can be expressed in terms of:  Mean(متوسط) arrival rate: mean number of jobs arriving per unit time, and  Mean service time: mean time taken to process each job  traffic intensity(كثافة): a single quantity(الكمية). the demand can be expressed as a single quantity known as the traffic intensity.

9. T305: DIGITAL COMMUNICATIONS 9 Arab Open University-Lebanon Tutorial 18 Topic 2: Specification Of Queues  Queues can be represented in diagrams like below  Jobs, join a queue by being stored in the buffer.  The jobs are in the form of digital data which can represent messages, packets, frames or anything that may require processing at any level in a layered hierarchy. The processing is done by the servers. A queuing system may have one or more servers, assumed to be all identical. A multiple-server queue is analogous to a single post office queue leading to several counters. Jobs waiting in the buffer move into a server as soon as one becomes free. If the buffer is empty and a server is free when a job arrives, it moves directly into the server. General representation of queues

10. T305: DIGITAL COMMUNICATIONS 10 Arab Open University-Lebanon Tutorial 18 Specifications of Queues  Jobs: digital data which can represent:  Messages, Packets, Frames or  Anything that may require processing at any level in a hierarchy.  Processing is done by the servers: A queueing system may have one or more identical (مطابق) servers  Jobs waiting in the buffer move into a server as soon as one becomes free.  If the buffer is empty and a server is free when a job arrives, it moves directly into the server.

11. T305: DIGITAL COMMUNICATIONS 11 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: Kendall( نسيج ) notation  A number of factors need to be specified before one can model ( صاغ ) a queuing system.  The Kendall notation takes the form: A/B/N/R  A is used to represent the arrival process,  B the service process,  N the number of servers and  R the maximum number of jobs that can be held in the queue as a whole.  In the case of a single server queue, if the buffer can hold one job, R = 2 because, when there is one job in the buffer, there must be another job being served. ServerBuffer ArrivalsDepartures

12. T305: DIGITAL COMMUNICATIONS 12 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: Kendall notation Poisson distributed: The probability distribution for the number of arrivals per unit time is given by what is known Poisson distribution. Poisson processes : is referred to memoryless arrival processes.  There are many possibilities for the arrival and service processes but the most common are represented by one of the three letters M, D or G.  M is used for random, memoryless (الذاكره), processes, that is Poisson distributed in the case of arrivals and negative exponential in the case of service. The M stands for Markov and these processes are often referred to as Markov processes.  D is used for deterministic(محدد مقرر), when fixed quantities are involved: where jobs arrive at regular intervals(فترات), PCM frames(Pulse Code Modulation ), for instance; or where there is a fixed service time, such as might be involved in processing constant-length packets.  G is used for general distributions, that is, any kind of distribution that is not generally memoryless.

13. T305: DIGITAL COMMUNICATIONS 13 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: Kendall notation  If the buffer is sufficiently (بما فيه الكفاية) big:  Probability (احتمال) of its filling up (يملأ) is negligible (لا تذكر).  Buffer is referred to as infinite and  R (number of jobs) symbol is omitted (حذف) FROM A/B/N/R.  When the Kendall A/B/N/R form is used,  ‘Service discipline (انضباط) ’ is assumed (يفترض) as first-in-first-out: when a server becomes free, the job at the front of the queue is the next one to be served.  Other possible disciplines – in particular (خاص), some jobs may have priority (الأولوية) and may ‘jump’ the queue.

14. T305: DIGITAL COMMUNICATIONS 14 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: Queue parameters and basic relations Notation for single-server queue  Figure above can be used to define some of the main parameters of a queue and to derive some of the basic relations between them:

15. T305: DIGITAL COMMUNICATIONS 15 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: Queue parameters and basic relations  Two relations are clear from above figure. They are:  Total mean time spent in the queue: Sum of the mean time jobs spend waiting in the buffer and the mean time they spend being served, that is:  Total mean number of jobs in the queue: Sum of the mean number waiting in the buffer and the mean number being served:  With a Single-server queue: the value of n s cannot exceed 1.  If server is idle (خامل) because there were no jobs waiting in the buffer when the previous job finished being served, the mean number served will be less than 1.

16. T305: DIGITAL COMMUNICATIONS 16 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: Queue parameters and basic relations  Little’s formula: Another set of relations.  It holds under very general conditions, for any arrival and service distributions, provided that all jobs entering the queue are served eventually.  Mean departure rate must equal the mean arrival rate.  For the total mean time in the system, t q, and number of jobs, n q, Little’s formula, applied to the whole queuing system, takes the form: where λ is the mean arrival rate.

17. T305: DIGITAL COMMUNICATIONS 17 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: Queue parameters and basic relations  When applied to the buffer section on its own, the formula is:  and for the server on its own:  The fraction of time during which the server is busy is called the server utilization (استخدام ),  (row), and, for a single-server queue, above equation can be rewritten as: or, since the service rate μ (meyoo), jobs per unit time, is equal to 1/t s :.t w  waiting time in buffer t a  is the mean time between arrivals λ  is the mean arrival rate(t a =1/ λ )..t s  is the mean service time µ  is the mean service rate(t s =1/µ).

18. T305: DIGITAL COMMUNICATIONS 18 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/M/1 Queues  These are queues with effectively (فعال) infinite buffers so that all jobs arriving at the queue are served eventually. The theoretical (نظري) model applies only if the server utilization  < 1.  The mean (متوسط) waiting time, t w, in the buffer and the mean number, n w, of jobs waiting in the buffer are given by:.t w  waiting time in buffer t a  is the mean time between arrivals λ  is the mean arrival rate(t a =1/ λ )..t s  is the mean service time µ  is the mean service rate(t s =1/µ).

19. T305: DIGITAL COMMUNICATIONS 19 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/M/1 Queues  The mean time, t q, jobs spend in the system (buffer + server) and the mean number, n q, of jobs in the system are given by:  The probability (احتمال) that the time spent in the system (buffer + server) by a job does not exceed time t is given by:(expression- مقدار جبري).t w  waiting time in buffer t a  is the mean time between arrivals λ  is the mean arrival rate(t a =1/ λ )..t s  is the mean service time µ  is the mean service rate(t s =1/µ).

20. T305: DIGITAL COMMUNICATIONS 20 Arab Open University-Lebanon Tutorial 18 CMA44 (Computer-Marked Assignment) Question 7 For an M/M/1 queue estimate the mean waiting time in the buffer if the mean service time is 0.33mS and the mean arrival rate is 1820 jobs per second. ts the service time is 0.33mS and, the mean arrival rate is 1520 jobs/second.  the occupancy ( الإشغال) of the server is.ts = 1820 * 0.33 = 0.6006 Using Equation 4.7 of the reference book = 0.492mS

21. T305: DIGITAL COMMUNICATIONS 21 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/G/1 and M/D/1 queues  In the case of M/G/1 queues, the mean waiting time in the buffer is given by:  Sigma= σ Where  s and t s are quantities which characterize ( وصف) the service distribution.  s has another mean related to the square ( مربع) of the service time. It is known as the standard deviation (الانحراف) for the service time.  And the mean number of jobs waiting for service in the buffer is:

22. T305: DIGITAL COMMUNICATIONS 22 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/G/1 and M/D/1 queues  For M/D/1 queues, the service time, t s, is constant and the standard deviation,  s, is zero, so the above two equations reduce to: for the mean waiting time in the buffer, and: for the mean number of jobs waiting for service in the buffer. Note that these are half the values of the corresponding (متطابق) means for M/M/1 queues.

23. T305: DIGITAL COMMUNICATIONS 23 Arab Open University-Lebanon Tutorial 18 CMA44 Question 9 Part of a router in packet-switching system consists of a single- server queue with an infinite buffer.Packet arrivals can be assumed to be a Poisson process with an arrival rate,, of 2000 packets per second. The service of 0.4ms is the same for all packets. Determine the mean waiting time in the buffer. The relevant section is again 4.2.4 M/D/1 (because ts is constant) of the Reference book. A deterministic system must be assumed with ts = 0.4ms and = 2000 jobs per second Thus  = * ts = 2000 * 0.4* 10-3 = 0.8 s and using equation 4.20 of the Reference Book

24. T305: DIGITAL COMMUNICATIONS 24 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/M/1/R queues – queues with finite buffers R stands for the maximum of jobs in the system. Buffer size =(R-1(in the server))*(Job size) (largest job size if they are not equally sized). If a job arrives and the buffer is full, we say that the job is blocked. In M/M/1 we assumed that all jobs joining the queue were served eventually, but in the case of finite buffer, this will not held. It is useful to introduce a new quantity called traffic intensity: A=λ/μ

25. T305: DIGITAL COMMUNICATIONS 25 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/M/1/R queues – queues with finite buffers  The traffic intensity, A, is defined as:  The server utilization is related to the traffic by:  The probability of blocking is:

26. T305: DIGITAL COMMUNICATIONS 26 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/M/1 Queues  The probability that there are exactly n jobs in the system (buffer + server) is:  The probability that there are at most n jobs in the system (buffer + server) is:  The probability that waiting time in the buffer does not exceed time t is:

27. T305: DIGITAL COMMUNICATIONS 27 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/M/1 Queues  The probability that there are at most n jobs waiting for service in the buffer is:  The value of t q required to ensure that r per cent of jobs do not wait longer than t r in the system is given by:  In designing for optimum (الأمثل) trade-off between the cost of having an idle (خامل) server in an M/M/1 queue and the cost of having jobs waiting in the buffer, the optimum utilization is given by: where the cost of having an idle server is a fraction, c, of the combined costs.

28. T305: DIGITAL COMMUNICATIONS 28 Arab Open University-Lebanon Tutorial 18 CMA44 Question 8 In an M/M/1 queueing system it is required that no more than 90% of the jobs should wait no longer than 5ms. Estimate the mean time that a job may spend in the system. See section 4.2.3 of the Reference Book tr is given as 5ms and r = 90. Using equation 4.16 of the reference book.

29. T305: DIGITAL COMMUNICATIONS 29 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/G/1 and M/D/1 queues  In the case of M/G/1 queues, the mean waiting time in the buffer is given by: Where  s and t s are quantities which characterize ( وصف) the service distribution.  s has another mean related to the square of the service time. It is known as the standard deviation (الانحراف المعياري) for the service time.  And the mean number of jobs waiting for service in the buffer is:

30. T305: DIGITAL COMMUNICATIONS 30 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/G/1 and M/D/1 queues  For M/D/1 queues, the service time, t s, is constant and the standard deviation,  s, is zero, so the above two equations reduce to: for the mean waiting time in the buffer, and: for the mean number of jobs waiting for service in the buffer. Note that these are half the values of the corresponding means for M/M/1 queues.

31. T305: DIGITAL COMMUNICATIONS 31 Arab Open University-Lebanon Tutorial 18 Specifications of Queues: M/M/1/R queues – queues with finite buffers  The mean number of jobs in the system (buffer + server) is: which can also be written as:  The waiting time in the system is:

32. T305: DIGITAL COMMUNICATIONS 32 Arab Open University-Lebanon Tutorial 18 CMA44 Question 10 An M/M/1/R queue is used to process call information. The amount of information required for each call is 984 bits. Estimate the minimum required buffer size, in bits, if the probability of blocking is not to exceed 0.001 when the traffic intensity is 0.75. We will use Equations 4.24 and 4.25 if of the reference book are used as they deal with the blocking probability of and M/M/1/R queue. R= Log(P b /(1-A) / log(A)) using the formula below. Buffer size=R*984 bits.

33. T305: DIGITAL COMMUNICATIONS 33 Arab Open University-Lebanon Tutorial 18 CMA44 Question 11 The mean traffic intensity presented to an M/M/1/6 queue is 0.75 erlang. The mean service time is 4ms. Determine the mean waiting time in the system. Equation 4.28 in the Reference Book can be applied. With R = 6 and A = 0.75

34. T305: DIGITAL COMMUNICATIONS 34 Arab Open University-Lebanon Tutorial 18 Topic 3: Quantifying Traffic ( قياس حركة المرور ) The traffic intensity or traffic, A, in a system can be defined in four equivalent ways: 1. The mean number of simultaneous calls, packets, messages, etc. (referred to as ‘calls’ for short) processed or carried by the system. 2. The traffic volume (sum of call durations) for a period T, divided by T: 1. The number of calls, n, in a period T, multiplied by the mean service time (holding time in the case of calls) and divided by T: 1. The arrival rate,, multiplied by the mean call-holding time, t s :

35. T305: DIGITAL COMMUNICATIONS What is An Erlang ? An Erlang is a unit of telecommunications traffic measurement. Strictly speaking, an Erlang represents the continuous use of one voice path. In practice, it is used to describe the total traffic volume of one hour. For example, if a group of user made 30 calls in one hour, and each call had an average call duration of 5 minutes, then the number of Erlangs this represents is worked out as follows: Minutes of traffic in the hour=number of calls x duration Minutes of traffic in the hour=30 x 5 Minutes of traffic in the hour=150 Hours of traffic in the hour=150 / 60 Hours of traffic in the hour=2.5 Traffic figure=2.5 Erlangs Erlang traffic measurements are made in order to help telecommunications network designers understand traffic patterns within their voice networks. 35 Arab Open University-Lebanon Tutorial 18

36. T305: DIGITAL COMMUNICATIONS 36 Arab Open University-Lebanon Tutorial 18 CMA44 Question 12 Table 1 represents the calls Logged (تسجيل) over a period of 20 minutes on a particular trunk route. Determine the mean traffic in erlangs over the period of observation. Using equation 4.29 of the Reference Book the traffic A is given by

37. T305: DIGITAL COMMUNICATIONS 37 Arab Open University-Lebanon Tutorial 18 Topic 4: Multiple-Server Queues  In an N-server queue with offered traffic A erlangs and blocking probability P B, the utilization, , of each server is:  The utilization for each server in an infinite-buffer N- server queue handling traffic A is:

38. T305: DIGITAL COMMUNICATIONS 38 Arab Open University-Lebanon Tutorial 18 Multiple-Server Queues: Loss systems  Loss systems consist of N servers but no buffer. The probability of blocking for an M/M/N/N loss system is given by the Erlang-B formula:  The following approximation (تقريب) gives the value of N required if the blocking probability is not to exceed 0.01, for a restricted range of traffic, A:

39. T305: DIGITAL COMMUNICATIONS 39 Arab Open University-Lebanon Tutorial 18 Multiple-Server Queues: Infinite-buffer queues  The mean waiting time in the buffer for M/M/N queues is given by: where E C (N, A) is known as the Erlang-C function. It is related to the Erlang-B function by the equation:

40. T305: DIGITAL COMMUNICATIONS 40 Arab Open University-Lebanon Tutorial 18 Multiple-Server Queues: Infinite-buffer queues  It is equal to the probability that a job should have to wait in the buffer because all the servers are busy at the time of its arrival. The mean number of customers waiting in the buffer of an M/M/N queue is:

41. T305: DIGITAL COMMUNICATIONS 41 Arab Open University-Lebanon Tutorial 18 Topic 5: Preparation for Next Tutorial Read Block 4 - Modelling Activities: Traffic Solve all exercises Overview the contents of the Systems and Processes Block 4, part 2: signaling.