{"title":"关于GIX/M/s/c队列的一些结果","authors":"F. Ferreira, A. Pacheco","doi":"10.1109/SAINTW.2005.106","DOIUrl":null,"url":null,"abstract":"We address the time dependent and steady-state analysis of the number of customers in a GIX/M/s/c queuing system at prearrivals of batches. As a corollary, we derive the continuous time steady-state distribution of the number of customers in the system in continuous time. The obtained closed form solutions are easy to compute, as they involve only combinatorial calculations and mixed-Poisson probabilities or mixed-Poisson expected values. Finally, the steady-state distribution of the number of customers seen by customers at their arrival to the system, blocking probability and mean and variance of the waiting times in queue of non-blocked costumers are derived.","PeriodicalId":220913,"journal":{"name":"2005 Symposium on Applications and the Internet Workshops (SAINT 2005 Workshops)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Results for GIX/M/s/c Queues\",\"authors\":\"F. Ferreira, A. Pacheco\",\"doi\":\"10.1109/SAINTW.2005.106\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We address the time dependent and steady-state analysis of the number of customers in a GIX/M/s/c queuing system at prearrivals of batches. As a corollary, we derive the continuous time steady-state distribution of the number of customers in the system in continuous time. The obtained closed form solutions are easy to compute, as they involve only combinatorial calculations and mixed-Poisson probabilities or mixed-Poisson expected values. Finally, the steady-state distribution of the number of customers seen by customers at their arrival to the system, blocking probability and mean and variance of the waiting times in queue of non-blocked costumers are derived.\",\"PeriodicalId\":220913,\"journal\":{\"name\":\"2005 Symposium on Applications and the Internet Workshops (SAINT 2005 Workshops)\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-01-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2005 Symposium on Applications and the Internet Workshops (SAINT 2005 Workshops)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SAINTW.2005.106\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2005 Symposium on Applications and the Internet Workshops (SAINT 2005 Workshops)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SAINTW.2005.106","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We address the time dependent and steady-state analysis of the number of customers in a GIX/M/s/c queuing system at prearrivals of batches. As a corollary, we derive the continuous time steady-state distribution of the number of customers in the system in continuous time. The obtained closed form solutions are easy to compute, as they involve only combinatorial calculations and mixed-Poisson probabilities or mixed-Poisson expected values. Finally, the steady-state distribution of the number of customers seen by customers at their arrival to the system, blocking probability and mean and variance of the waiting times in queue of non-blocked costumers are derived.