Diletta Olliaro , Marco Ajmone Marsan , Simonetta Balsamo , Andrea Marin
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We categorize jobs into two classes: the first class consists of jobs that only require one server, while the second class includes jobs that require a larger number of servers. We obtain the system utilization and the throughput of the two job classes for the case in which the number of servers requested by jobs in the second class is equal to the number of available servers, using a simple approach that allows for a general distribution of the service time of jobs in the second class. Hence, we derive the stability condition of the non-saturated MJQM under these assumptions. Additionally, we develop an approximate analysis for the case in which the jobs of the second class require a fraction of the available servers.</p><p>Based on analytical and numerical results, we highlight interesting system properties and insights.</p></div>","PeriodicalId":19964,"journal":{"name":"Performance Evaluation","volume":"162 ","pages":"Article 102370"},"PeriodicalIF":1.0000,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The saturated Multiserver Job Queuing Model with two classes of jobs: Exact and approximate results\",\"authors\":\"Diletta Olliaro , Marco Ajmone Marsan , Simonetta Balsamo , Andrea Marin\",\"doi\":\"10.1016/j.peva.2023.102370\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>We consider a multiserver queue where jobs request for a varying number of servers for a random service time. The requested number of servers is assigned to each job following a First-In First-Out (FIFO) order. When the number of free servers is not sufficient to accommodate the next job in line, that job and any subsequent jobs in the queue are forced to wait. As a result, not all available servers are allocated to jobs if the next job requires more servers than are currently free. This queuing system is often called a </span><span><em>Multiserver Job </em><em>Queuing Model</em></span> (MJQM).</p><p>In this paper, we study the behavior of a MJQM under saturation, i.e., when the waiting line always contains jobs to be served. We categorize jobs into two classes: the first class consists of jobs that only require one server, while the second class includes jobs that require a larger number of servers. We obtain the system utilization and the throughput of the two job classes for the case in which the number of servers requested by jobs in the second class is equal to the number of available servers, using a simple approach that allows for a general distribution of the service time of jobs in the second class. Hence, we derive the stability condition of the non-saturated MJQM under these assumptions. 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The saturated Multiserver Job Queuing Model with two classes of jobs: Exact and approximate results
We consider a multiserver queue where jobs request for a varying number of servers for a random service time. The requested number of servers is assigned to each job following a First-In First-Out (FIFO) order. When the number of free servers is not sufficient to accommodate the next job in line, that job and any subsequent jobs in the queue are forced to wait. As a result, not all available servers are allocated to jobs if the next job requires more servers than are currently free. This queuing system is often called a Multiserver Job Queuing Model (MJQM).
In this paper, we study the behavior of a MJQM under saturation, i.e., when the waiting line always contains jobs to be served. We categorize jobs into two classes: the first class consists of jobs that only require one server, while the second class includes jobs that require a larger number of servers. We obtain the system utilization and the throughput of the two job classes for the case in which the number of servers requested by jobs in the second class is equal to the number of available servers, using a simple approach that allows for a general distribution of the service time of jobs in the second class. Hence, we derive the stability condition of the non-saturated MJQM under these assumptions. Additionally, we develop an approximate analysis for the case in which the jobs of the second class require a fraction of the available servers.
Based on analytical and numerical results, we highlight interesting system properties and insights.
期刊介绍：
Performance Evaluation functions as a leading journal in the area of modeling, measurement, and evaluation of performance aspects of computing and communication systems. As such, it aims to present a balanced and complete view of the entire Performance Evaluation profession. Hence, the journal is interested in papers that focus on one or more of the following dimensions:
-Define new performance evaluation tools, including measurement and monitoring tools as well as modeling and analytic techniques
-Provide new insights into the performance of computing and communication systems
-Introduce new application areas where performance evaluation tools can play an important role and creative new uses for performance evaluation tools.
More specifically, common application areas of interest include the performance of:
-Resource allocation and control methods and algorithms (e.g. routing and flow control in networks, bandwidth allocation, processor scheduling, memory management)
-System architecture, design and implementation
-Cognitive radio
-VANETs
-Social networks and media
-Energy efficient ICT
-Energy harvesting
-Data centers
-Data centric networks
-System reliability
-System tuning and capacity planning
-Wireless and sensor networks
-Autonomic and self-organizing systems
-Embedded systems
-Network science
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