Queueing Theory and its BusinessS Applications

Queueing Theory and its BusinessS Applications

1. Queueing Theory Presented to : Dr. Dibyojyoti Bhattacharjee Presented by : Biswajit Bhattacharjee (19) Bikash Choudhury (16) Biswaraj Das Purkayastha (20) Kunal Sengupta (37)

2. Introduction to Queueing Theory A pioneer: Agner Krarup Erlang (1878-1929 ) the Danish telecommunication engineer started applying principles of queuing theory in the area of telecommunications.

3. What is queueing theory? Queueing theory is the mathematical study of waiting lines, or queues. In queueing theory a model is constructed so that queue lengths and waiting times can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service. Queueing theory has its origins in research by Agner Krarup Erlang when he created models to describe the Copenhagen telephone exchange. The ideas have since seen applications including telecommunications, traffic engineering, computing and the design of factories, shops, offices and hospitals.

4. Why is queueing theory important? Capacity problems are very common in industry and one of the main drivers of process redesign Need to balance the cost of increased capacity against the gains of increased productivity and service Queuing and waiting time analysis is particularly important in service systems Large costs of waiting and of lost sales due to waiting Example – Hospital Patients arrive by ambulance or by their own accord One doctor is always on duty More and more patients seeks help  longer waiting times Question : Should another MD position be instated?

5. 5 Commercial Queuing Systems Commercial organizations serving external customers Ex. Dentist, bank, ATM, gas stations, plumber, garage … Transportation service systems Vehicles are customers or servers Ex. Vehicles waiting at toll stations and traffic lights, trucks or ships waiting to be loaded, taxi cabs, fire engines , buses … Business-internal service systems Customers receiving service are internal to the organization providing the service Ex. Inspection stations, conveyor belts, computer support … Social service systems Ex. Judicial process, hospital , waiting lists for organ transplants or student dorm rooms … Examples of Real World Queuing Systems?

6. 6 Problems of a store manger When and why do we get queues? What can we do about it? More cash desks What if there are too many desks open? Let on more people in  First serve the people who need little service time Limit the time during which someone is being served Too many people, too few desks  costs  e.g. limited treatment time per client at the doctor

7. 7 Problems of a customer Why does it always feel to us like all other queues move faster? Which queue should I take? Where shall I append? How long do I have to wait? Where there are the fewest people in queue? Where the people have the least products to dispatch? Where the fastest cashier is? Where one can only pay cash? Where someone helps me bagging ?

8. Queuing theory for studying networks View network as collections of queues FIFO data-structures Queuing theory provides probabilistic analysis of these queues Examples: Average length (buffer) Average waiting time Probability queue is at a certain length Probability a packet will be lost

9. Use Queuing models to Describe the behavior of queuing systems Evaluate system performance Model Queuing System Queuing System Queue Server Customers

10. Time Time Arrival event Delay Begin service Begin service Arrival event Delay Activity Activity End service End service Customer n +1 Customer n Interarrival

11. Assumptions Independent arrivals Exponential distributions • Customers do not leave or change queues. • Large queues do not discourage customers. Many assumptions are not always true, but queuing theory gives good results anyway

12. Measuring the Queue Performance There are a number of measure that can help a manager to balance the capacity and waiting costs: Average time in a queue Average length of a queue Average customer time in the system Number of customers in a queue Probability of numbers in a queue Probability of system being unused The last two above, looking at probability is where most of the work on queue theory goes on You will need to understand more about statistics, particularly Poisson distribution) to delve deeper into this

13. 13 Components of a Basic Queuing Process Calling Population Queue Service Mechanism Input Source The Queuing System Jobs Arrival Process Queue Configuration Queue Discipline Served Jobs Service Process leave the system

14. 14 Principal Queue Parameters Calling Population Arrival Process Service Process Number of Servers Queue Discipline

15. 15 1. The Calling Population Population of customers or jobs The size can be finite or infinite The latter is most common Can be homogeneous Only one type of customers/ jobs Or heterogeneous Several different kinds of customers/jobs

16. 16 2. Arrival Process In what pattern do jobs / customers arrive to the queueing system? Distribution of arrival times? Batch arrivals? Finite population? Finite queue length? Poisson arrival process often assumed Many real-world arrival processes can be modeled using a Poisson process

17. 17 3. Service Process How long does it take to service a job or customer? Distribution of arrival times? Rework or repair? Service center (machine) breakdown? Exponential service times often assumed Works well for maintenance or unscheduled service situations

18. 18 4. Number of Servers How many servers are available? Single Server Queue Multiple Server Queue

19. 19 Example – Two Queue Configurations Servers Multiple Queues Servers Single Queue

20. 20 The service provided can be differentiated Ex. Supermarket express lanes Labor specialization possible Customer has more flexibility Balking behavior may be deterred Several medium-length lines are less intimidating than one very long line Guarantees fairness FIFO applied to all arrivals No customer anxiety regarding choice of queue Avoids “cutting in” problems The most efficient set up for minimizing time in the queue Jockeying (line switching) is avoided Multiple vs Single Customer Queue Configuration Multiple Line Advantages Single Line Advantages

21. 21 5. Queue Discipline How are jobs / customers selected from the queue for service? First Come First Served (FCFS) Shortest Processing Time (SPT) Earliest Due Date (EDD) Priority (jobs are in different priority classes) FCFS default assumption for most models

22. Three queuing disciplines used in Telephone Networks First In First Out – This principle states that customers are served one at a time and that the customer that has been waiting the longest is served first. Last In First Out – This principle also serves customers one at a time, however the customer with the shortest waiting time will be served first. Processor Sharing – Customers are served equally. Network capacity is shared between customers and they all effectively experience the same delay

23. FIFO “First In First Out”

24. LIFO “Last in First Out” Elevators are a circumstance where this occurs.

25. SIRO “Service In Random Order” Like drawing tickets out of a pool of tickets for service.

26. Single-server Single-stage Queue Service Facility Customers In queue Arrival Stream

27. Multiple-server Single-stage Queue Service Facilities Customers In queue

28. Single-server Multiple-stage Queue Service Facility Customers In queue Pharmacy Conveyor System >>>>>

29. Multiple-server Multiple-Stage Queue Service Facilities Customers In queue

30. Types of Queues of Interest Analytical Models for Estimating Capacity and Related Metrics Single Server M/M/1, M/G/1, M/D/1, G/G/1 Multiple Server M/M/c, M/G/ ∞ etc. Multiple Stage Markov Chain models

31. Infinite-Source Queuing Models Single channel, exponential service time (M/M/1) Single channel, constant service time (M/D/1) Multiple channel, exponential service time (M/M/S) Multiple priority service, exponential service time

32. BUSINESS APPLICATIONS It is a practical operations management technique that is commonly used to determine staffing, scheduling and calculating inventory levels. To improve customer satisfaction. Six Sigma professionals – through their knowledge of probability distributions, process mapping and basic process improvement techniques – can help organizations design and implement robust queuing models to create this competitive advantage. Timeliness: Businesses conduct studies using mathematical models and formulas to determine the best way of serving the greatest number of customers, given their staffing resources. In retail businesses, the volume of transactions is extremely important in maximizing revenues and profitability Remove Inefficiencies: for eg ., bank, needs to stick to its model once it's been determined that maximum efficiency can be achieved, both in labor costs and customers served, by using a centralized queue based on staffing at least three tellers during peak hours.

33. The assumptions of classical queuing theory may be too restrictive to be able to model real-world situations exactly. The complexity of production lines with product-specific characteristics cannot be handled with those models. Often, although the bounds do exist, they can be safely ignored. Because the differences between the real-world and theory is not statistically significant, as the probability that such boundary situations might occur is remote compared to the expected normal situation. Furthermore, several studies show the robustness of queuing models outside their assumptions. In other cases the theoretical solution may either prove intractable or insufficiently informative to be useful. Alternative means of analysis have thus been devised in order to provide some insight into problems that do not fall under the scope of queuing theory, A lthough they are often scenario-specific because they generally consist of computer analysis of experimental data. 33 Limitations of Queuing theory

34. Primary References http://en.wikipedia.org/wiki/Queueing_theory http://www.eventhelix.com/realtimemantra/congestioncontrol/queueing_theory.htm http://people.brunel.ac.uk/~mastjjb/jeb/or/queue.html http://people.brunel.ac.uk/~mastjjb/jeb/or/queue.html http://www.merriam-webster.com/dictionary/queuing%20theory http://www.amazon.com/Fundamentals-Queueing-Theory-Probability-Statistics/dp/047179127X http://staff.um.edu.mt/jskl1/simweb/intro.htm