For making a single-channel, single-phase queuing model, which of the following assumptions are involved?

(A) Every arrival waits to be served regardless of the length of time.
(B) Arrivals are independent of preceding arrivals, but the average number of arrivals does not change over time.
(C) Arrivals come from a finite or very small population on a LIFO basis.
(D) Service times follow the negative exponential distribution or are constant.
(E) The average service rate is greater than the average arrival rate.

Choose the correct answer from the options given below:

Correct option is C

A single-channel, single-phase queuing model is a basic queuing system where customers arrive, wait in a queue (if necessary), receive service from a single server, and then depart. The assumptions involved in this model include:

• (A) Every arrival waits to be served regardless of the length of time:
  This is a valid assumption in basic queuing models, as customers do not leave before receiving service.

• (B) Arrivals are independent of preceding arrivals, but the average number of arrivals does not change over time:
  This follows a Poisson process, where arrivals occur randomly but with a consistent average rate over time.

• (D) Service times follow the negative exponential distribution or are constant:
  In queuing theory, service times often follow a negative exponential distribution, meaning short service times are more frequent, but longer service times are still possible.

• (E) The average service rate is greater than the average arrival rate:
  For a stable system, the service rate (μ) must be greater than the arrival rate (λ). If λ ≥ μ, the queue will grow indefinitely.

Information Booster:

• Poisson Arrivals: Most queuing models assume customer arrivals follow a Poisson process, meaning they occur randomly but with a stable average rate.

• Negative Exponential Service Times: This distribution is common in service processes, where short service times are more likely than long ones.

• First-Come, First-Served (FCFS): Basic queuing models assume that service is provided on an FCFS basis, meaning every arrival will eventually be served.

• Traffic Intensity Condition (ρ = λ/μ): A system is stable when ρ < 1, meaning the service rate exceeds the arrival rate.

• Single-Phase Queuing: A single-phase model means each customer undergoes only one stage of service before leaving the system.

• Single-Channel System: This refers to only one server handling all arrivals, making efficient service rate management crucial.

Additional Knowledge:

• (C) Arrivals come from a finite or very small population on a LIFO basis:
  This is incorrect because most queuing models assume an infinite population and service is usually provided on a FIFO (First In, First Out) basis, not LIFO (Last In, First Out).