Steady-state operations of the various queuing systems refer to the situation when:
a. Ordinarily expected customer arrival and service patterns occur.
b. The arrival and service processes are deterministic.
c. There is high variability in customer departure patterns.
d. There is high variability in customer arrival patterns.
The correct answer and explanation is :
The correct answer is:
a. Ordinarily expected customer arrival and service patterns occur.
Explanation:
Steady-state operations in queuing systems refer to the long-run behavior of the system when the transient effects of initial conditions have dissipated. In this state, the system reaches a statistical equilibrium where key performance metrics such as average queue length, waiting times, and utilization rates remain stable over time.
Why Option A is Correct
Ordinarily expected customer arrival and service patterns imply that the queuing system has settled into a predictable and stable mode. This means that the system operates under typical conditions where the arrival rate and service rate fluctuate within expected limits but maintain an overall balance. The system is neither overwhelmed with excessive demand nor significantly underutilized.
Why Other Options Are Incorrect
- Option B: “The arrival and service processes are deterministic.”
- In real-world queuing systems, arrival and service rates are typically stochastic (random), following probability distributions such as Poisson for arrivals and exponential for service times. A deterministic system (where arrivals and services occur at fixed intervals) is a special case and does not define steady-state operations.
- Option C: “There is high variability in customer departure patterns.”
- High variability in customer departures suggests instability rather than steady-state operation. If service times fluctuate excessively, queues may experience frequent congestion or idle periods, preventing the system from achieving equilibrium.
- Option D: “There is high variability in customer arrival patterns.”
- High arrival variability can lead to unpredictable queue lengths and waiting times, disrupting steady-state operations. While some variation is normal, excessive fluctuations prevent the system from maintaining stable performance.
Thus, steady-state operation means the system has settled into an expected and stable pattern of arrivals and services, making option A the correct choice.