Abstract
A new flexible discipline for providing priority to one of two types of customers in a single-server queue is proposed. This discipline assumes the use of additional finite storages for each type of arriving customer. During the stay in a storage, a customer can leave the system or transfer to the main infinite buffer. Preference to priority customers is provided via the proper choice of the rates of a customer transfer from the storages to the buffer. Analysis of this discipline is implemented under quite general assumptions about the arrival and service processes. The advantage of the proposed discipline over the classical non-preemptive discipline is numerically demonstrated.
Highlights
Queueing theory provides a powerful tool for the optimization of sharing the restricted resources in many telecommunication, manufacturing, logistic, social, and other systems and networks.In particular, it has wide applications for optimization of routing and energy saving in modern networks where heterogeneous information flows have to be delivered from one node to another one with minimal delay and energy consumption; see, e.g., [1,2,3,4,5,6,7]
In polling disciplines, which assume a cyclic connection of the common server to the buffers designed for storing different types of customers, priority can be provided to some type of customers via more frequent connection to the buffer for storing the priority customers and via a longer duration of maintaining this connection
The generalized processor sharing discipline is the generalization of the usual processor sharing discipline, which assumes that all customers present in the system receive service simultaneously with the rate inversely proportional to the number of these customers
Summary
Queueing theory provides a powerful tool for the optimization of sharing the restricted resources in many telecommunication, manufacturing, logistic, social, and other systems and networks. A low priority customer can have a very long waiting time and succeed to start service essentially later than the priority customer that arrived only recently; see, e.g., [8] In this respect, the dynamical priorities, which take into account the types of customers present in the system, and the lengths of the corresponding queues, are much more flexible. We propose and analyze another reasonable mechanism for customer admission to service that is more flexible than the strict non-preemptive priority The idea of this mechanism is to introduce some auxiliary storages for the preliminary storing of the different types of arriving customers before their admission to the main buffer. They highlight the impact of customer transfer rates from the storages to the buffer on the performance measures of the system and illustrate the possibility of the optimal choice of the rates to minimize the weighted loss functions including the probabilities of customer loss in the storages and in the buffer (due to impatience)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
