Towards a Balance Between Energy Savings and Quality of Service: a Finite-Buffer Queueing Model with a Controlled Machine Vacation

The problem of energy savings is today a key challenge in the process of designing service systems and their control mechanisms. On the one hand, the aim is to make maximum use of the technical and operational capabilities of the service station. On the other hand, however, it requires periodic technical inspections and maintenances, which causes its temporary immobilization and suspension of the job (customer, packet, call, etc.) service process. In the paper, we propose a queueing model of service process with finite accumulation buffer capacity in which a mechanism of energy saving is implemented based on single vacation policy. Namely, each time when the system empties the service station begins a vacation period of random duration in which the service process is blocked to save the energy. During the vacation period the service station can be maintained but, in some cases, it also can process secondary jobs then. The vacation period, however, may be shortened if the number of jobs accumulated in the buffer is close to its maximum capacity. Such an approach allows to achieve a balance between energy savings and ensuring appropriate quality of service (minimizing the risk of job losses due to buffer overflow). The explicit-form analytic representation for the queue-size distribution in the considered system will be found using the approach based on the idea of embedded Markov chain and linear algebra. Numerical examples illustrating the impact on key system input parameters on the queue-size distribution will be attached, as well.