- 2072 Ashwin · 5+5 marks
Queuing characteristics and application
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.
What are the characteristics of a queuing system? Discuss any one practical application of queuing system.
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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