Asymptotic Analysis of Resource Heterogeneous QS $$ (\mathrm {MMPP}+2\mathrm {M})^{(2,\nu )}/\mathrm {GI}(2)/\infty $$ under Equivalently Increasing Service Time
Аннотация
We consider a resource heterogeneous queuing system with a flexible two-node request-response facility. Each node has a certain resource capacity for service (buffer space) and hence a potential to respond to an incoming demand that generates a request for the provision of some random amount of resources for some random time. The request flows are steady-state Poisson flows of varying intensity. If it is required to use the resources of both nodes to serve a request, then it is assumed that the moments of arrival of such requests form an MMPP flow with a division into two different types of requests. A distinctive feature of the systems under consideration is that the resource is released in the same amount as requested. To construct a multidimensional Markov process, we use the method of introducing an additional variable and dynamic probabilities. The problem of analyzing the total capacity of customers of each type is solved provided that the request servicing intensity is much lower than the incoming flow intensity and assuming that the servers have unlimited resources.