Optimal Control Problems for Erlang Loss Systems
An Erlang loss system, which is an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>/</mo><mi>G</mi><mo>/</mo><mi>s</mi><mo>/&...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/2/130 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | An Erlang loss system, which is an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>/</mo><mi>G</mi><mo>/</mo><mi>s</mi><mo>/</mo><mi>s</mi></mrow></semantics></math></inline-formula> queue, is a model used in various applications. In this paper, a controlled version of the process is defined. The objective is to maximize the expected time until the system is full when the service time is exponentially distributed. The control variable is the service rate. The dynamic programming equation satisfied by the value function <i>F</i>, from which the optimal control follows at once, is derived, and <i>F</i> is found explicitly when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>s</mi><mo>=</mo><mn>3</mn></mrow></semantics></math></inline-formula>. The problem of minimising the probability of the system being saturated is also considered. |
|---|---|
| ISSN: | 2075-1680 |