- 2070 Bhadra · 2.5+5+2.5 marks
Queuing characteristics; M/D/6/10/FIFO
Short answer
Key characteristics: calling population, arrival process, service mechanism, queue discipline, system capacity, customer behavior. Kendall's notation A/B/c/K/N/Z: A=inter-arrival distribution, B=service distribution, c=servers, K=capacity, N=population, Z=discipline; defaults are infinite capacity/population and FIFO. M/D/6/10/FIFO: Poisson arrivals, constant service time, 6 servers, capacity 10, FIFO.
Mention the characteristics of a queuing system. Explain the Kendall's notation in queuing systems. What is the meaning of M/D/6/10/FIFO in queuing system?
Characteristics of a queuing system
- Calling population: finite or infinite source of customers.
- Arrival process: distribution of inter-arrival times; single or batch arrivals.
- Service mechanism: distribution of service times; number of servers.
- Queue discipline: FIFO, LIFO, SIRO or priority.
- System capacity: limit on the number in the system.
- Customer behaviour: balking, reneging, jockeying.
Kendall's notation
Kendall's notation writes a queue as A/B/c/K/N/Z, so that any queue can be named in one line.
| 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 |
Omitted fields mean infinite capacity, infinite population and FIFO. Examples:
- M/M/1: Poisson arrivals, exponential service, one server (single-counter shop).
- M/M/c: same with c parallel servers (bank with several tellers).
- M/G/1: Poisson arrivals, general service time, one server (CPU).
- M/D/1: constant service time (automatic car wash).
Meaning of M/D/6/10/FIFO
| Field | Meaning |
|---|---|
| M | Poisson arrivals |
| D | Constant service time |
| 6 | Six servers in parallel |
| 10 | System capacity of 10 customers (6 in service, at most 4 waiting) |
| FIFO | Customers are served in order of arrival |
Calling population is infinite since it is not stated. Example: a six-lane toll plaza where every vehicle takes a fixed time to pay, with room for only 10 vehicles in the plaza; vehicles beyond that are turned away.
✓ Answer checked by Claude Opus 5.5 (high effort)
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