--- title: "Queuing characteristics and application" subject: "Simulation and Modeling" chapter: 4 key: "semester_8/simulation_and_modeling:queuing-characteristics-application" source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/queuing-characteristics-application site: BCT Engineering --- # Queuing characteristics and application Simulation and Modeling · Chapter 4: Queuing system - Asked in: 2072 Ashwin, 5+5 marks - Video: [CHARACTERISTICS OF QUEUEING SYSTEMS ( SIMULATION & MODELING )](https://www.youtube.com/watch?v=6FShQ4ez728) — Aqib Naeem - 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-application - Whole chapter: https://www.bctengineer.com/md/semester_8/simulation_and_modeling/chapter-4 ## Question What are the characteristics of a queuing system? Discuss any one practical application of queuing system. ## Short answer Characteristics: calling population (finite/infinite), arrival pattern, service mechanism, number of servers, queue discipline (FIFO, LIFO, priority), capacity, customer behaviour (balking, reneging). Practical application: bank with three tellers, M/M/3 model, Poisson arrivals 45/hr, exponential service 20/hr per teller, utilisation 0.75, used for staffing and wait-time analysis. ## Answer #### Characteristics of a queuing system A queuing system is a place where customers arrive, wait for service and leave. It is described by the following characteristics. | Characteristic | Description | |---|---| | Calling population | Source of customers; finite (150 machines) or infinite (public arriving at a bank). A finite source means arrival rate depends on how many are already in the system. | | Arrival pattern | Distribution of inter-arrival times (usually Poisson/exponential); single or batch arrivals; arrivals may be scheduled or random. | | Customer behaviour | Balking (refusing to join a long queue), reneging (leaving after waiting), jockeying (switching to a shorter queue). | | Service mechanism | Distribution of service time (exponential, constant, general); single or batch service. | | Number of servers | One server or many in parallel; servers in series form a multi-stage (tandem) system. | | Queue discipline | Rule for choosing the next customer: FIFO, LIFO, SIRO (random), priority, shortest job first. | | System capacity | Maximum number allowed in the system; infinite or finite. When full, new arrivals are lost. | | Queue configuration | One common queue for all servers, or a separate queue for each server. | Common performance measures are average number in queue (Lq), average waiting time (Wq), server utilisation (rho = lambda / (c * mu)) and probability that the system is empty or full. #### Practical application: bank counter Take a branch of a bank in Kathmandu with three teller windows and one common line. - **Calling population**: infinite (any member of the public). - **Arrivals**: random, about 45 customers per hour (Poisson). - **Service**: exponential, average 3 minutes per customer, so each teller can serve 20 customers per hour. - **Servers**: three tellers in parallel, one common queue, FIFO. This is an M/M/3 queue. - **Utilisation**: rho = 45 / (3 x 20) = 0.75, so the tellers are busy 75% of the time. Using the queuing model (or a simulation of it), the manager can find the average waiting time, the longest queue, and what happens if a fourth teller is added or if arrivals rise at month end. The result guides staffing: too few tellers give long waits and lost customers, too many waste salary. The same method is used for hospital OPDs, call centres, toll booths, airport check-in and CPU or network packet scheduling. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is balking? A. Refusing to join a long queue B. Leaving after waiting for a time C. Switching to a shorter queue D. Being served in batches Answer: A. Balking is not joining; reneging is leaving after waiting; jockeying is switching queues. (Key point: Customer behaviour) 2. What is the effect of a finite calling population? A. Arrivals become deterministic B. The arrival rate depends on how many customers are already in the system C. The queue capacity becomes infinite D. Service time becomes constant Answer: B. With a finite source, customers already in the system cannot arrive again, so the arrival rate changes. (Key point: Finite population) 3. For 3 tellers, each serving 20/hour, with 45 arrivals/hour, what is rho = lambda/(c mu)? A. 0.45 B. 1.50 C. 0.75 D. 0.15 Answer: C. rho = 45/(3 x 20) = 0.75, so tellers are busy 75% of the time. (Key point: Utilisation) 4. How does the bank manager use the queuing model or simulation? A. To fix the arrival rate of customers B. To eliminate all queues C. To measure the salary of tellers only D. To find waiting times and test staffing, such as adding a fourth teller Answer: D. The model shows how waits change with more tellers or higher arrivals, guiding staffing without disturbing the real system. (Key point: Use of the model) ## Related in Simulation and Modeling - [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 - [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 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 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 - [Queuing block diagram; M/M/4 and D/M/2](https://www.bctengineer.com/question.md?key=semester_8%2Fsimulation_and_modeling%3Aqueuing-block-diagram-mm4) — Simulation and Modeling, chapter 4 ## Related in other subjects - [Practical IA characteristics; optical isolation](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aia-practical-characteristics-optical) — Advanced Electronics, chapter 4 - [Queuing system and Kendall's notation](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aqueuing-system-kendall) — Telecommunications, chapter 6, asked 4× - [Short note: Queuing theory in delay system](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Ashort-note-queuing-delay) — Telecommunications, chapter 6 - [Application, system and device domain](https://www.bctengineer.com/question.md?key=semester_8%2Fmultimedia_system%3Aapplication-system-device-domain) — Multimedia System, chapter 1