--- title: "Queuing block diagram; M/M/4 and D/M/2" subject: "Simulation and Modeling" chapter: 4 key: "semester_8/simulation_and_modeling:queuing-block-diagram-mm4" source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/queuing-block-diagram-mm4 site: BCT Engineering --- # Queuing block diagram; M/M/4 and D/M/2 Simulation and Modeling · Chapter 4: Queuing system - Asked in: 2074 Bhadra, 6+2+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-block-diagram-mm4 - Whole chapter: https://www.bctengineer.com/md/semester_8/simulation_and_modeling/chapter-4 ## Question Define queuing system with block diagram and its uses. Explain M/M/4/20/2000/FCFS and D|M|2|LIFO|18 system. ## Short answer A queuing system models customers arriving, waiting, and being served. Block diagram: calling population -> queue -> server(s) -> departures. Uses: teller staffing, CPU scheduling, traffic control. M/M/4/20/2000/FCFS: Poisson arrivals, exponential service, 4 servers, capacity 20, finite population 2000, first-come first-served. D|M|2|LIFO|18: deterministic inter-arrivals, exponential service, 2 servers, last-in first-out, capacity 18, infinite population. ## Answer #### Queuing system A **queuing system** is a system in which customers arrive for service, wait in a queue if all servers are busy, receive service and depart. It is described by the arrival pattern, the service pattern, the number of servers, capacity and queue discipline. #### Block diagram ```text Calling arrivals +-------+ +----------+ population ---------->| Queue |---->| Server(s)|--> Departures (source) +-------+ +----------+ waiting line service |<----------------- Queuing system ------------>| ``` Customers who find the system full are turned away (lost). Customers may also refuse to join a long queue (balk) or leave after waiting for some time (renege). #### Uses - Planning the number of tellers, counters, doctors or machines. - Computer systems: CPU scheduling, printers, disk requests, network routers and packet delay. - Telephone exchanges and call centres. - Traffic signals, airports and toll booths. - Manufacturing lines and inventory handling. - Estimating waiting time, queue length and utilization, and checking simulation models. #### M/M/4/20/2000/FCFS Following the pattern `A/B/c/K/N/D`: - M: Poisson (random) arrivals, exponential inter-arrival times. - M: exponential service times. - 4: four parallel servers. - 20: the system capacity is 20, so at most 20 customers (4 in service and 16 waiting); further arrivals are turned away. - 2000: the calling population is finite, 2000 possible customers. - FCFS: first come first served. #### D|M|2|LIFO|18 - D: deterministic (constant) inter-arrival time. - M: exponential service time. - 2: two servers. - LIFO: last in first out; the most recently arrived waiting customer is served next. - 18: system capacity is 18 customers. - The calling population is not given, so it is taken as infinite. (The order of the last fields differs from the standard Kendall order, but each field is identified by its meaning.) ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In the block diagram, what path does a customer follow? A. Calling population, then queue, then server(s), then departure B. Server, then queue, then calling population C. Queue, then calling population, then server D. Calling population, then server, then queue Answer: A. Customers arrive from the source, wait in the queue if servers are busy, are served and depart. (Key point: Queuing system structure) 2. In M/M/4/20/2000/FCFS, what does 20 mean? A. 20 servers in parallel B. System capacity: at most 20 customers (4 in service and 16 waiting) C. 20 minutes mean service time D. A calling population of 20 Answer: B. The fourth field is capacity; with 4 servers, 16 can wait and further arrivals are turned away. (Key point: M/M/4/20/2000/FCFS capacity) 3. What does 2000 mean in M/M/4/20/2000/FCFS? A. 2000 customers per hour arrive B. The queue can hold 2000 customers C. A finite calling population of 2000 possible customers D. 2000 seconds is the service time Answer: C. The fifth field is the size of the calling population. (Key point: M/M/4/20/2000/FCFS population) 4. In D|M|2|LIFO|18, which statement is correct? A. Poisson arrivals, constant service, 2 servers, oldest customer first, capacity 18 B. Constant arrivals, exponential service, 18 servers, LIFO, capacity 2 C. Exponential arrivals and service, 2 servers, FCFS, population 18 D. Constant inter-arrival time, exponential service, 2 servers, newest waiting customer served first, capacity 18 Answer: D. D = deterministic arrivals, M = exponential service, LIFO serves the latest arrival first, and 18 is the capacity (population taken as infinite). (Key point: D|M|2|LIFO|18) ## Related in Simulation and Modeling - [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 model, Kendall, M/D/8/15/LIFO](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-model-mdlifo-8) — Simulation and Modeling, chapter 4 - [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 system usefulness and types](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-types-usefulness) — Simulation and Modeling, chapter 4 - [Short note: Application of queuing system](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Ashort-note-queuing-application) — Simulation and Modeling, chapter 4 - [Five GPSS block diagram symbols](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Agpss-block-symbols) — Simulation and Modeling, chapter 9, asked 2× ## Related in other subjects - [Block diagram of digital communication system](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Ablock-diagram-digital-comm) — Data Communication, chapter 1, asked 8× - [Communication system and block diagram](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Acomm-system-block-diagram) — Basic Electronics Engineering, chapter 5, asked 7× - [Closed loop control system block diagram explained](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Awhat-is-cs-bd-closed-loop) — Control Systems, chapter 1, asked 4× - [Instrumentation system with block diagram](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Ainstrumentation-system) — Basic Electronics Engineering, chapter 7, asked 3×