Analysis of Discrete-Time Queues with Branching Arrivals
We consider a discrete-time single server queueing system, where arrivals stem from a multi-type Galton–Watson branching process with migration. This branching-type arrival process exhibits intricate correlation, and the performance of the corresponding queueing process can be assessed analytically....
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-02-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/4/1020 |
| _version_ | 1797619463546208256 |
|---|---|
| author | Dieter Fiems Koen De Turck |
| author_facet | Dieter Fiems Koen De Turck |
| author_sort | Dieter Fiems |
| collection | DOAJ |
| description | We consider a discrete-time single server queueing system, where arrivals stem from a multi-type Galton–Watson branching process with migration. This branching-type arrival process exhibits intricate correlation, and the performance of the corresponding queueing process can be assessed analytically. We find closed-form expressions for various moments of both the queue content and packet delay. Close inspection of the arrival process at hand, however, reveals that sample paths consist of large independent bursts of arrivals followed by geometrically distributed periods without arrivals. Allowing for non-geometric periods without arrivals, and correlated bursts, we apply <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula>-thinning on the arrival process. As no closed-form expressions can be obtained for the performance of the corresponding queueing system, we focus on approximations of the main performance measures in the light and heavy traffic regimes. |
| first_indexed | 2024-03-11T08:28:28Z |
| format | Article |
| id | doaj.art-83e85a1f3abe4309ba2f430e4ff3bf24 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T08:28:28Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-83e85a1f3abe4309ba2f430e4ff3bf242023-11-16T21:57:15ZengMDPI AGMathematics2227-73902023-02-01114102010.3390/math11041020Analysis of Discrete-Time Queues with Branching ArrivalsDieter Fiems0Koen De Turck1Department Telin, Ghent University, B-9000 Gent, BelgiumDepartment Telin, Ghent University, B-9000 Gent, BelgiumWe consider a discrete-time single server queueing system, where arrivals stem from a multi-type Galton–Watson branching process with migration. This branching-type arrival process exhibits intricate correlation, and the performance of the corresponding queueing process can be assessed analytically. We find closed-form expressions for various moments of both the queue content and packet delay. Close inspection of the arrival process at hand, however, reveals that sample paths consist of large independent bursts of arrivals followed by geometrically distributed periods without arrivals. Allowing for non-geometric periods without arrivals, and correlated bursts, we apply <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula>-thinning on the arrival process. As no closed-form expressions can be obtained for the performance of the corresponding queueing system, we focus on approximations of the main performance measures in the light and heavy traffic regimes.https://www.mdpi.com/2227-7390/11/4/1020discrete-time queuearrival correlationbranching process |
| spellingShingle | Dieter Fiems Koen De Turck Analysis of Discrete-Time Queues with Branching Arrivals Mathematics discrete-time queue arrival correlation branching process |
| title | Analysis of Discrete-Time Queues with Branching Arrivals |
| title_full | Analysis of Discrete-Time Queues with Branching Arrivals |
| title_fullStr | Analysis of Discrete-Time Queues with Branching Arrivals |
| title_full_unstemmed | Analysis of Discrete-Time Queues with Branching Arrivals |
| title_short | Analysis of Discrete-Time Queues with Branching Arrivals |
| title_sort | analysis of discrete time queues with branching arrivals |
| topic | discrete-time queue arrival correlation branching process |
| url | https://www.mdpi.com/2227-7390/11/4/1020 |
| work_keys_str_mv | AT dieterfiems analysisofdiscretetimequeueswithbranchingarrivals AT koendeturck analysisofdiscretetimequeueswithbranchingarrivals |