--- title: "Queuing model, Kendall, M/D/8/15/LIFO" subject: "Simulation and Modeling" chapter: 4 key: "semester_8/simulation_and_modeling:queuing-model-mdlifo-8" source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/queuing-model-mdlifo-8 site: BCT Engineering --- # Queuing model, Kendall, M/D/8/15/LIFO Simulation and Modeling · Chapter 4: Queuing system - Asked in: 2071 Bhadra, 5+2.5+2.5 marks - Video: [Kendall’s Notation in Queuing System | Simulation and Modeling | IOE](https://www.youtube.com/watch?v=FvmGlMIaGTk) — Engivault - 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-model-mdlifo-8 - Whole chapter: https://www.bctengineer.com/md/semester_8/simulation_and_modeling/chapter-4 ## Question What is the model of a queuing system? What do you mean by Kendall's notation in queuing systems? What is the meaning of M/D/8/15/LIFO in queuing system? Explain. ## Short answer A queuing model describes customer flow through arrival, queue, service, and departure. Kendall notation: A/B/c/K/N/Z, where A inter-arrival dist, B service dist, c servers, K capacity, N population, Z discipline. M/D/8/15/LIFO: Poisson arrivals, deterministic service, 8 servers, capacity 15, last-in first-out discipline, infinite population. ## Answer #### Model of a queuing system A **queuing model** represents a system in which customers arrive from a calling population, join a queue if all servers are busy, are served by one or more servers and then depart. It is defined by its arrival process, service time distribution, number of servers, system capacity and queue discipline. The model is analysed mathematically (for simple cases) or simulated to find waiting time, queue length and utilisation. ```text Arrivals +-----------------+ +--------+ Departures (calling --> | Queue (waiting | --> | Server | --> population) | line, buffer) | | (s) | +-----------------+ +--------+ queue discipline service (FIFO, LIFO...) time dist. ``` #### Kendall's notation Kendall's notation is a standard short code, **A/B/c/K/N/Z**, that names the type of a queue. | Symbol | Position | Meaning | Common codes | |---|---|---|---| | A | 1st | Inter-arrival time distribution | M (exponential), D (deterministic), Ek (Erlang), G (general) | | B | 2nd | Service time distribution | M, D, Ek, G | | c | 3rd | Number of parallel servers | 1, 2, 3, ... | | K | 4th | System capacity (queue + service) | finite number or infinity | | N | 5th | Size of calling population | finite number or infinity | | Z | 6th | Queue discipline | FIFO, LIFO, SIRO, PRI | If the last fields are left out, the defaults are infinite capacity, infinite population and FIFO. Example: M/M/1 is a single-server queue with Poisson arrivals and exponential service. #### Meaning of M/D/8/15/LIFO - **M**: arrivals are Poisson (exponential inter-arrival times). - **D**: service time is deterministic (constant for every customer). - **8**: eight identical servers working in parallel. - **15**: system capacity is 15, meaning at most 15 customers can be in the system (8 in service and 7 waiting). A 16th arrival is turned away. - **LIFO**: the last customer to arrive is served first when a server becomes free. - Calling population is not written, so it is infinite. Example: a warehouse with eight loading bays, a fixed loading time per truck and room for only 15 trucks in the yard; the newest truck in the yard is handled first. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What defines a queuing model? A. Arrival process, service time distribution, number of servers, capacity and discipline B. Only the number of servers C. Only the arrival rate D. Only the size of the building Answer: A. A model is defined by those five elements. (Key point: Queuing model) 2. If the last fields of Kendall notation are omitted, what are the defaults? A. Capacity 1, population 1 and LIFO B. Infinite capacity, infinite population and FIFO C. Infinite capacity, finite population and FIFO D. Zero capacity and random discipline Answer: B. Omitted fields default to infinity, infinity and FIFO. (Key point: Defaults) 3. In M/D/8/15/LIFO, how many customers can wait in the queue? A. 15 B. 8 C. 7 (capacity 15 with 8 in service) D. 23 Answer: C. Capacity is the total in the system, so waiting room is 15 - 8 = 7; the 16th arrival is turned away. (Key point: M/D/8/15/LIFO capacity) 4. Why is the calling population of M/D/8/15/LIFO taken as infinite? A. Because LIFO needs infinite population B. Because D means infinite C. Because 8 servers cannot have a finite source D. It is not written, so the default of infinity applies Answer: D. Unstated population defaults to infinite. (Key point: Population) ## Related in Simulation and Modeling - [Queuing system, characteristics, Kendall notation](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-characteristics-role-kendall) — Simulation and Modeling, chapter 4, asked 2× - [Queuing model; M/D/2/60/150/FIFO meaning](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-model-mdpq-kendall) — Simulation and Modeling, chapter 4 - [Queuing characteristics; D/M/1/LIFO/20/510](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-dmlifo-application) — Simulation and Modeling, chapter 4 - [Queuing notation, default values, elements](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-notation-defaults-elements) — Simulation and Modeling, chapter 4 - [Queuing characteristics; M/D/6/10/FIFO](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-characteristics-mdfifo-6) — Simulation and Modeling, chapter 4 - [Queuing system usefulness and types](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-types-usefulness) — Simulation and Modeling, chapter 4 ## Related in other subjects - [Kendall-Lee notation for queuing systems](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Akendall-lee-notation) — Telecommunications, chapter 6, asked 2× - [Queuing system and Kendall's notation](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aqueuing-system-kendall) — Telecommunications, chapter 6, asked 4× - [Erlang delay model: notation and derivation](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aerlang-delay-kendall-derivation) — Telecommunications, chapter 6 - [Queuing theory in delay systems](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aqueuing-theory-delay-systems) — Telecommunications, chapter 6