Three Preemptive Priority Policies

This discussion is a continuation of Non-preemptive vs. Preemptive Priority Queue Disciplines. A preemptive queue discipline can take one or more of the following three policies: preemptive-resume, preemptive-repeat-identical, and preemptive-repeat-different.

Preemptive-Resume

This policy says that the service of an item in a queue can be preempted by a higher-priority item such that the service of the lower-priority item will be paused until the service of the higher-priority item is completed and will then be resumed from where the service was paused.

Think of an emergency room in a hospital. Patients with varying degrees of emergencies can enter the emergency room at any given time, and some emergencies, such as a life-threatening injury, preempt medical attention over a non-life-threatening emergency. If a patient with a non-life-threatening injury were being tended to by the emergency staff and a life-threatening injury were to enter the emergency room, the medical staff would pause the medical attention being given to the patient with the non-life-threatening injury and would redirect attention to the patient with the life-threatening injury.

Preemptive-Repeat-Identical

This policy says that the service of an item in a queue can be preempted by a higher-priority item such that the service of the lower-priority item will be paused until the service of the higher-priority item is completed and will then restart with an identical service period to that of the original service period.

Think of a customer service queue in which no call notes are collected per caller and shared with other representatives during the transfer of the caller from one representative to another. If a caller takes 2 minutes to explain the purpose of the call to the first representative, who tells the caller that resolving the issue would take approximately 5 minutes, but the center receives a higher-priority call from a caller who was designated as, say, a VIP customer, then the first caller would either be placed on hold until the next available representative is available or transferred to another available representative for service. Because caller notes are not taken, the caller would have to reexplain the purpose of the call from the beginning and the next representative would then provide the 5-minute service to resolve the issue, assuming that no other VIP customers call for service. The lower-priority caller’s service would restart from the beginning with an identical service period.

Preemptive-Repeat-Different

This policy says that the service of an item in a queue can be preempted by a higher-priority item such that the service of the lower-priority item will be paused until the service of the higher-priority item is completed and will then restart with a different service period to that of the original service period.

Think of an airplane pilot who contacted the air traffic controller to request permission to land. As the pilot was approaching the runway, another pilot declared an emergency and requested permission to land. The pilot who declared the emergency is a higher priority than the pilot who did not declare an emergency. The controller would require the lower-priority pilot to slow down or execute a minor go around so to clear the approach for the pilot with the emergency. Whereas the pilot without the emergency had to have the approach delayed due to the emergency landing of the other pilot, the pilot does not necessarily have to restart the approach. It could be the case that the pilot without the emergency can resume landing from a point along the approach rather than having to execute the approach from the beginning. The second approach might only take 7 minutes instead of the original 10 minutes.

Further Reading

Chang, W. (1965). Preemptive priority queues. Operations Research, 13(5), 820-287. https://www.jstor.org/stable/167731

Chang, W. (1965). Queueing with nonpreemptive and preemptive-resume priorities. Operations Research, 13(6), 1020-1022. https://www.jstor.org/stable/167660

Fralix, B. (2024). On the time-dependent behavior of preemptive single-server queuing systems with Poisson arrivals. Queuing Syst, 107, 31-61. https://doi.org/10.1007/s11134-024-09905-2

Takács, L. (1965). Priority queues. Operations Research, 12(1), 63-74. https://www.jstor.org/stable/167753

Walraevens, J., Fiems, D., & Bruneel, H. (2006). The discrete-time preemptive repeat identical priority queue. Queuing Syst, 53, 231-243. https://doi.org/10.1007/s11134-006-7770-x