--- title: "Queuing characteristics; D/M/1/LIFO/20/510" subject: "Simulation and Modeling" chapter: 4 key: "semester_8/simulation_and_modeling:queuing-dmlifo-application" source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/queuing-dmlifo-application site: BCT Engineering --- # Queuing characteristics; D/M/1/LIFO/20/510 Simulation and Modeling · Chapter 4: Queuing system - Asked in: 2072 Magh, 5+3+2 marks - 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-dmlifo-application - Whole chapter: https://www.bctengineer.com/md/semester_8/simulation_and_modeling/chapter-4 ## Question What are the characteristics of a queuing system? What is the meaning of D/M/1/LIFO/20/510 in queuing system? Write down the application of queue. ## Short answer Characteristics: calling population, arrival pattern, service mechanism, number of servers, queue discipline, capacity, customer behaviour. D/M/1/LIFO/20/510: deterministic inter-arrivals, exponential service, 1 server, last-in first-out discipline, capacity 20, finite population 510. Applications: banks, CPU scheduling, call centres, traffic control, manufacturing. ## Answer #### Characteristics of a queuing system A queuing system has customers who arrive, wait if needed, get service and depart. Its main characteristics are: 1. **Calling population**: finite or infinite source of customers. 2. **Arrival pattern**: distribution of inter-arrival times (Poisson, constant, general), single or batch arrivals. 3. **Customer behaviour**: balking, reneging and jockeying. 4. **Service pattern**: service time distribution (exponential, constant, general). 5. **Number of servers**: single or multiple; parallel or in series. 6. **Queue discipline**: FIFO, LIFO, SIRO, priority. 7. **System capacity**: maximum number in the system, infinite or finite. 8. **Queue layout**: one shared queue or one queue per server. #### Meaning of D/M/1/LIFO/20/510 The standard Kendall order is arrival / service / servers / capacity / population / discipline (A/B/c/K/N/Z). Here the discipline is written in the fourth place, so the code is read as: | Field | Meaning | |---|---| | D | Deterministic arrivals: customers arrive at fixed, equal intervals | | M | Markovian service: exponentially distributed service times | | 1 | A single server | | LIFO | Last in, first out: the newest waiting customer is served first | | 20 | Maximum of 20 customers in the system at a time (if read as capacity) | | 510 | Calling population of 510 customers (finite source) | Example: a machine feeds items into a stack at regular intervals; a single worker picks the top (latest) item, taking a random time. The stack holds at most 20 items, and the items come from 510 possible units. (Some books place the last two numbers in the order population / capacity; the idea is the same: one is the capacity and the other is the population.) #### Applications of queues - Banks, ticket counters and supermarket checkouts. - Computer systems: CPU scheduling, disk requests, print spooling and network packet buffers. - Telephone exchanges and call centres. - Hospitals (OPD, emergency), traffic signals and toll plazas. - Manufacturing: jobs waiting for machines on an assembly line. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which is a characteristic of a queuing system? A. Queue discipline such as FIFO, LIFO, SIRO or priority B. The colour of the server C. The programming language of the simulation D. The total revenue of the facility Answer: A. Queue discipline is one of the main characteristics, along with population, arrival pattern, service, servers and capacity. (Key point: Characteristics) 2. In D/M/1/LIFO/20/510, what do D and M mean? A. Exponential arrivals and constant service B. Deterministic (fixed interval) arrivals and exponential service times C. Deterministic discipline and Markov servers D. Delayed arrivals and multiple servers Answer: B. The first field is the arrival distribution, D = deterministic; the second is service, M = exponential. (Key point: Meaning of D and M) 3. What does LIFO mean in this system? A. The oldest waiting customer is served first B. Customers are served at random C. The newest waiting customer is served first D. High priority customers go first Answer: C. Last in, first out serves the most recent arrival. (Key point: Discipline) 4. In this non-standard order, what are 20 and 510? A. 20 = servers, 510 = capacity B. 20 = population, 510 = arrival rate C. 20 = mean service time, 510 = capacity D. 20 = maximum customers in the system, 510 = calling population Answer: D. The answer reads 20 as capacity and 510 as the finite calling population, noting books may swap the order. 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