--- title: "Queuing system, characteristics, Kendall notation" subject: "Simulation and Modeling" chapter: 4 key: "semester_8/simulation_and_modeling:queuing-characteristics-role-kendall" source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/queuing-characteristics-role-kendall site: BCT Engineering --- # Queuing system, characteristics, Kendall notation Simulation and Modeling · Chapter 4: Queuing system - Asked in: 2073 Bhadra, 2+2+2+4 marks; 2070 Magh, 2+2+2+4 marks (asked 2 times) - Video: [Queuing Theory Tutorial - Queues/Lines, Characteristics, Kendall Notation, M/M/1 Queues](https://www.youtube.com/watch?v=SqSUJ0UYWMQ) — Bikey Bonn Kleiford Seranilla - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/queuing-characteristics-role-kendall - Whole chapter: https://www.bctengineer.com/md/semester_8/simulation_and_modeling/chapter-4 ## Question What is a queuing system? List the various characteristics of a queuing system. Explain the role of queuing system in simulation study. Explain Kendall notation with example. ## Short answer A queuing system involves customers, a queue, and servers. Characteristics include arrival/service distributions, number of servers, queue discipline, and capacity. In simulation, queuing models provide waiting times and utilization for complex systems; analytical formulas like M/M/1 aid validation. Kendall notation A/B/c/K/N/D: M/M/1 denotes Poisson arrivals, exponential service, one server. ## Answer #### Queuing system A **queuing system** consists of customers (arrivals) who come to a service facility, wait in a queue if the server is busy, are served, and then leave. Examples: bank counter, hospital OPD, CPU job queue, traffic at a signal. #### Characteristics of a queuing system 1. **Calling population:** the source of customers; finite or infinite. 2. **Arrival process:** how customers arrive (usually Poisson, so exponential inter-arrival times), singly or in batches. 3. **Service mechanism:** distribution of service times and number of servers (single or multiple, parallel or in series). 4. **Queue discipline:** the rule for choosing the next customer: FCFS, LIFO, priority, random. 5. **System capacity:** maximum number allowed in the queue (finite or infinite). 6. **Customer behaviour:** balking (not joining), reneging (leaving after waiting), jockeying (changing queues). 7. **Number of service stages:** single stage or several in series. #### Role in simulation study - Many systems studied by simulation (banks, computer networks, CPUs, factories, traffic) are queuing systems, so queue models are the building blocks of discrete-event simulation. - Simulation provides performance measures such as average waiting time, queue length, server utilization and probability of delay, when the distributions are too complex for formulas. - Analytical formulas (M/M/1, M/M/c) give a quick estimate to **verify and validate** the simulation model. - It allows what-if studies, e.g. effect of adding a server, without disturbing the real system. #### Kendall notation A queue is described by `A/B/c/K/N/D`: | Symbol | Meaning | |---|---| | A | Inter-arrival time distribution | | B | Service time distribution | | c | Number of parallel servers | | K | System capacity (default infinity) | | N | Size of calling population (default infinity) | | D | Queue discipline (default FCFS) | Distribution codes: **M** = Markovian (Poisson arrivals or exponential times), **D** = deterministic (constant), **E_k** = Erlang with k phases, **G** = general (any distribution). **Example 1:** `M/M/1` is Poisson arrivals, exponential service, one server, infinite capacity and population, FCFS. With arrival rate 4/hour and service rate 6/hour: utilization 0.667, average number in system 2, average time in system 0.5 hour. **Example 2:** `M/D/3/50` is Poisson arrivals, constant service time, 3 servers, at most 50 customers in the system, infinite population, FCFS. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which behaviour describes a customer leaving the queue after waiting for some time? A. Reneging B. Balking C. Jockeying D. Blocking Answer: A. Reneging is leaving after waiting; balking is not joining; jockeying is switching queues. (Key point: Queue characteristics) 2. Why are analytical formulas such as M/M/1 useful in a queue simulation study? A. They replace the need for any simulation B. They give a quick estimate to verify and validate the simulation model C. They generate the random numbers for arrivals D. They fix the number of servers automatically Answer: B. Formulas for simple queues are compared with simulation output to check the model is correct. (Key point: Role in simulation) 3. In A/B/c/K/N/D, what do the fields c and K represent? A. c = calling population, K = number of servers B. c = queue discipline, K = capacity C. c = number of parallel servers, K = system capacity D. c = service time distribution, K = population Answer: C. The third field is servers and the fourth is the maximum number of customers in the system. (Key point: Kendall notation) 4. In Kendall notation what are the default values of K, N and D? A. Zero, infinity and LIFO B. Infinity, 1 and priority C. Finite, finite and FCFS D. Infinity, infinity and FCFS Answer: D. If omitted, capacity and population are infinite and discipline is FCFS. 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