TB MC Qu. 10-31 A constant arrival distribution...

A constant arrival distribution is which of the following?

Question

TB MC Qu. 10-31 A constant arrival distribution...

A constant arrival distribution is which of the following?

BlackTom AI · Accepted Answer

Question restatement: TB MC Qu. 10-31 A constant arrival distribution... A constant arrival distribution is which of the following?

Option A: Variable, with customers arriving at fixed time throughout the arrival window. Here, the wording is contradictory: 'variable' suggests the interarrival times are not fixed, while 'fixed time' implies a consistent spacing. The mismatch makes this option incorrect for describing a constant arrival distribution.

Option B: Periodic, with random times between successive arrivals. If times between arrivals are random, the interarrival gaps are not fixed. 'Periodic' implies regular, repeating intervals, so this option cannot describe a constant arrival distribution and is therefore false.

Option C: Variable, with random times between successive arrivals. This describes a stochastic process with unpredictable gaps, not a constant interarrival time. Since a constant arrival distribution requires uniform gaps, this choice is incorrect.

Option D: Sometimes variable and sometimes periodic. A constant arrival distribution does not alternate between variable and periodic in a single definition; it has a single, fixed interarrival pattern. Thus, this option mischaracterizes the distribution.

Option E: Periodic, with exactly the same time between successive arrivals. This option captures the essence of a constant interarrival distribution: arrivals occur at regular, equal intervals, which corresponds to a constant interarrival time. The terms 'periodic' and 'exactly the same time between arrivals' align with the definition of a constant arrival distribution.

Summary of reasoning across options: The key idea is whether the interarrival times are fixed or variable. Only the option describing equal, regular gaps between arrivals satisfies a constant arrival distribution. All other options introduce variability, randomness, or mixed behavior that contradicts the notion of a constant interarrival interval.

TB MC Qu. 10-31 A constant arrival distribution... A constant arrival distribution is which of the following?

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