{"title":"On optimal and equilibrium retrial rates in an unreliable retrial queue with two types of customers","authors":"Feng Zhang, Jinting Wang","doi":"10.1145/2021216.2021246","DOIUrl":"https://doi.org/10.1145/2021216.2021246","url":null,"abstract":"A single-server retrial queue with two types of customers in which the server is subject to breakdowns and repairs is studied. Two types of customers arrive to the system in accordance with two different independent Poisson flows. There is no waiting space in front of the server and therefore, if the server is found busy or down, the blocked two types of customers form two sources of repeated calls. The service times of the two types of customers have two different independent general distributions. It is also assumed that the server has a service-type dependent exponentially distributed lifetime as well as a service-type dependent, generally distributed repair time. Explicit expressions are derived for the expected number of retrial customers of each type. In addition, by assuming both types of customers face linear costs for waiting and conducting retrials, we discuss and compare optimal and equilibrium retrial rates respectively regarding the situations in which the customers are cooperative or noncooperative.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130516747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A feed back retrial queueing system with two types of arrivals","authors":"N. Thillaigovindan, R. Kalyanaraman","doi":"10.1145/2021216.2021242","DOIUrl":"https://doi.org/10.1145/2021216.2021242","url":null,"abstract":"A retrial queueing system with two types of customers and with feed back is considered. Type 1 customers arrive in batches of size k with probability ck and type 2 customers arrive singly according to two Poisson processes with rates [EQUATION] and λ2 respectively. Service time distri butions are different for both type of customers. If arriving customers are blocked due to server being busy, type 1 customers are queued in a priority queue of infinite capacity, while type 2 customers enter into a retrial group in order to seek service again after a random amount of time. For this system the joint distribution of the number of customers in the priority queue and in the retrial group is obtained in closed form. Some operating characteristics are derived and a numerical study is also carried out.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"2014 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127599744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A decomposition result for single server discrete-time queues with generalized vacations","authors":"S. D. Clercq, B. Steyaert, H. Bruneel","doi":"10.1145/2021216.2021222","DOIUrl":"https://doi.org/10.1145/2021216.2021222","url":null,"abstract":"For several specific discrete-time queueing models with a vacation policy, the stationary system occupancy at the beginning of a random slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. This paper aims to show that this decomposition can be applied to for a large class of discrete-time queueing systems with vacations. The analysis builds on results obtained by Fuhrmann and Cooper concerning continuous-time queueing systems with Poissonian arrivals. Through some examples we show that the queueing analysis can be considerably simplified using this decomposition property.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115301860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Performance analysis of a slotted multi-channel MAC protocols for cognitive radio networks","authors":"Kyung Jae Kim, Jin Soo Park, Y. Bae, B. Choi","doi":"10.1145/1837856.1837878","DOIUrl":"https://doi.org/10.1145/1837856.1837878","url":null,"abstract":"Cognitive radio has emerged as one of effective methods to enhance utilization of radio spectrum. Main principle of cognitive radio is that the secondary users (SUs) are allowed to use the spectrum not used by primary users (PUs) without interfering PU's transmission. In this paper, we consider network system where PUs use channels under super-slot time structure and SUs content to access channels during unused super-slot so as not to interfere PU's transmission. For contention resolution, super-slot is divided into slots of fixed size which are used as backoff unit for backoff algorithm. For contending SUs, our proposed MAC protocol operates by the following modified CSMA/CA with binary backoff algorithm: Each SU uniformly chooses a backoff counter from the current backoff window. The backoff counter indicates the number of slots that the station has to wait before the transmission. At the beginning of super-slot, SU senses pre-determined number of channels. If there are no idle channels, then the backoff counter of the SU is frozen during a current super-slot duration. If there are idle channels, then the SU decrements its backoff counter by one per each time slot as long as time slot is idle. When the backoff counter of the SU reaches zero, the SU transmits the packets as many of fixed size as idle channels accommodate in the current super-slot. During backoff procedure of the SU, if other SUs occupy the remaining idle channels, backoff counter of the SU is frozen during the remaining part of super-slot and is reactivated when at least one channel is sensed idle at the beginning of the super-slot. We construct the three-dimensional discrete time Markov chain (DTMC) to investigate the performance of the proposed multi-channel MAC protocol and we obtain stationary probability vector of DTMC by censored Markov chain's method. Then, using the stationary probability vector of DTMC, we obtain the head of line (HoL) packet delay distribution and the normalized throughput of SUs.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115320162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tail asymptotics for waiting time distribution of an M/M/s queue with general impatient time","authors":"Y. Sakuma, A. Inoie, K. Kawanishi, M. Miyazawa","doi":"10.1145/1837856.1837877","DOIUrl":"https://doi.org/10.1145/1837856.1837877","url":null,"abstract":"In this paper, we consider an M/M/s queue where customers may abandon waiting for service and renege the system without receiving their services. We assume that impatient time on waiting for each customer is independent and identically distributed non-negative random variable with a general distribution where the probability distribution is light-tailed and unbounded. The main objective of this paper is to provide an approximation for the waiting time distribution in an analytically tractable form. To this end, we obtain the tail asymptotics of the waiting time distributions of served and impatient customers. By using the tail asymptotics, we show that the fairly good approximations of the waiting time distributions can be obtained with low numerical complexity.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128287654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Performance analysis for the Geom/G/1 queue with single working vacation","authors":"Xiu-li Xu, Yance Li, N. Tian","doi":"10.1145/1837856.1837858","DOIUrl":"https://doi.org/10.1145/1837856.1837858","url":null,"abstract":"In this paper, we analyzed a Geom/G/1 queue with single working vacation. Firstly, we obtained the M/G/1-type structure matrix of the two-dimensional embedded Markov chain. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived. Furthermore, we got the stochastic decomposition formulae for the PGF of the stationary queue size and the stationary waiting time. Finally, several numerical examples are presented to verify these results.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127904429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Performance of an efficient sleep mode operation for IEEE 802.16m","authors":"S. Baek, B. Choi","doi":"10.1145/1837856.1837871","DOIUrl":"https://doi.org/10.1145/1837856.1837871","url":null,"abstract":"Power saving is one of the important issues for battery-powered mobile station in mobile WiMAX. Both IEEE 802.16e and IEEE 802.16m standards define sleep mode operations for power saving of mobile stations. In IEEE 802.16e, sleep mode alternates the listening window of fixed length and the sleep window where the sleep window can be doubled. The mobile station sends or receives packets during the active mode. In IEEE 802.16m, sleep cycle consists of extendable listening window and sleep window where sleep cycle can be doubled and the sleep window is the remaining part of sleep cycle. The mobile station sends or receives the data during the extendable listening window without going back to the active mode. The extendable listening window is implemented by T_AMS timer which plays the role of sleep mode request/response messages in the IEEE 802.16e. In this paper, we propose an efficient sleep mode operation for IEEE 802.16m advanced mobile WiMAX. The proposed scheme takes advantages of sleep modes in both IEEE 802.16e and IEEE 802.16m. This scheme has binary exponential sleep windows which guarantee the minimum length for effective power saving. The mobile station uses the T_AMS timer in IEEE 802.16m so that the mobile station sends or receives data packets during the extendable listening window in the sleep mode. We mathematically analyze the proposed scheme by an embedded Markov chain to obtain the average message delay and the average power consumption of a mobile station. The analytical results match with the simulation results very well. The analytical results show that the power consumption of our scheme is better than those of the legacy sleep modes in the IEEE 802.16e and the IEEE 802.16m under the same delay bound.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130252112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cost optimization of an M/M/r queueing system with queue-dependent servers: genetic algorithm","authors":"J. Ke, J. Ke, Chuen-Horng Lin","doi":"10.1145/1837856.1837869","DOIUrl":"https://doi.org/10.1145/1837856.1837869","url":null,"abstract":"We consider an M/M/r queueing system with infinite capacity, in which the number of working servers changes depending on the queue length. The steady-state probability distributions and the expected number of customers in the system are derived, which are used to construct a cost function. In order to minimize the expected cost of the system, we use the genetic algorithm to find the best thresholds of queue length in activating servers and their corresponding service rate. Some illustrative examples are provided to demonstrate how the process of this algorithm works for the optimal management policy of the multi-server queueing system.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130460246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dropping behavior of a random early detection mechanism by a queueing model of batch arrivals and multiple servers","authors":"H. Luh, Chia-Hung Wang, Chung-Min Lin","doi":"10.1145/1837856.1837867","DOIUrl":"https://doi.org/10.1145/1837856.1837867","url":null,"abstract":"With the emerging popularity of multimedia applications, quality of service on Internet becomes an important issue. Random Early Detection (RED) is one of the most widely used adaptive queue management in the Internet. In this paper, we extend the basic concept and study an analytic model for RED queues with batch arrival and multiple servers. A Markovian approach is presented in order to study different quality metrics by RED parameters, such as batch sizes, dropping rates, etc. Numerical results obtained by simulation and analytic methods illustrate those performance measures of the proposed RED queue, such as average system/queue sizes, average sysetm/queue waiting time, average dropping probability.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"2013 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114881130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tuan Phung-Duc, H. Masuyama, S. Kasahara, Yutaka Takahashi
{"title":"A simple algorithm for the rate matrices of level-dependent QBD processes","authors":"Tuan Phung-Duc, H. Masuyama, S. Kasahara, Yutaka Takahashi","doi":"10.1145/1837856.1837864","DOIUrl":"https://doi.org/10.1145/1837856.1837864","url":null,"abstract":"We develop a simple algorithm to compute the rate matrices of ergodic level-dependent quasi-birth-and-death processes, based on a matrix continued fraction representation and a probabilistic interpretation of those matrices. The algorithm is easier to implement and less memory-consuming than that developed by Bright and Taylor. We apply the algorithm to an infinite-server queueing system with a Markovian arrival process and exponentially distributed service times. We present some numerical results in order to demonstrate the efficiency of our algorithm.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"258 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132083702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}