RUDN University mathematicians have proposed a model for a service system in which one server processes multiple request streams. Unlike analogues, new model forbids to interrupt the operating of the request, even if the time allocated for the stream, in which it arrives, has expired. The results can be used, for example, in banking. The study is published in Mathematics.

 A "polling" type system is a mathematical model in which one performer (or server) executes several requests from different users in some order. It is used in telecommunications, production organization, traffic management and other areas. Initially, the model was invented to describe the work of an equipment repairman ona factory. Usually, such models assume the customers are impatient. This means that if a request is not processed for some time, then it leaves the queue. RUDN University mathematicians have proposed a new approach to polling systems. In it, a request that has been received for service cannot be interrupted it until it is processed. In practice, this is implemented, for example, in banking.

“In certain systems, the customers are absolutely patient and depart from the system only after receiving the service. Consideration of the model analyzed in this paper was originated during the implementation of applied research to optimize the work of the inter-banking processing center of the Republic of Belarus, which handles all money transactions between the banks. In modeling the inter-banking processing center, any financial transaction accepted for processing in the center must be implemented and committed”, said  Alexander Dudin, PhD, Director of Research Center from the Institute of Applied Mathematics and Telecommunication, RUDN.

In the model proposed by the RUDN University mathematicians, customers come to the system in the Markov flow allowing dependence of inter-arrival times. After that, new customers go to the "waiting room", buffer. It is assumed that the server alternates the work and rest periods. The server operation time is limited. If there are no customers in the system, then the rest period begins. At the same time, if the working time has expired, but the processing of the application has not ended, the server cannot go to rest. The duration of the "vacation" and work is distributed according to the phase law, which is significantly more general than the exponential law popular in the literature. 

RUDN University mathematicians studied the resulting model and determined the conditions for its stability, as well as formulas for calculating the main indicators of the system (waiting time, the probability that a new application will fall on the server rest time, etc).

“Our model is built under pretty general assumptions about the probabilistic distributions describing the behavior of the system and the realistic assumption, in many real-world systems, that ongoing service cannot be terminated ahead of schedule. The stationary distribution of the system states, as well as the waiting time distribution of an arbitrary customer, are obtained. This distribution is interesting from the perspective of the application of the results of the investigation of the considered vacation queueing model to the analysis of polling systems”, said Alexander  Dudin,


Journal Link: Mathematics 2021, 9(13), 1508