Loading...
Please wait, while we are loading the content...
Similar Documents
Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers
| Content Provider | MDPI |
|---|---|
| Author | Efrosinin, Dmitry Stepanova, Natalia |
| Copyright Year | 2021 |
| Description | In this paper, we study the problem of optimal routing for the pair of two-server heterogeneous queues operating in parallel and subsequent optimal allocation of customers between the servers in each queue. Heterogeneity implies different servers in terms of speed of service. An open-loop control assumes the static resource allocation when a router has no information about the state of the system. We discuss here the algorithm to calculate the optimal routing policy based on specially constructed Markov-modulated Poisson processes. As an alternative static policy, we consider an optimal Bernoulli splitting which prescribes the optimal allocation probabilities. Then, we show that the optimal allocation policy between the servers within each queue is of threshold type with threshold levels depending on the queue length and phase of an arrival process. This dependence can be neglected by using a heuristic threshold policy. A number of illustrative examples show interesting properties of the systems operating under the introduced policies and their performance characteristics. |
| Starting Page | 2766 |
| e-ISSN | 22277390 |
| DOI | 10.3390/math9212766 |
| Journal | Mathematics |
| Issue Number | 21 |
| Volume Number | 9 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2021-10-31 |
| Access Restriction | Open |
| Subject Keyword | Mathematics Operations Research and Management Science Parallel Queues Open-loop Policy Markov Decision Process Threshold Policy Matrix-analytic Approach Difference Equations |
| Content Type | Text |
| Resource Type | Article |
