In this paper,we consider the impatient customers in M/M/1 queueing model under variant working vacation policy.The customer’s impatience is due to its arrival during a working vacation period,where the service rate ...In this paper,we consider the impatient customers in M/M/1 queueing model under variant working vacation policy.The customer’s impatience is due to its arrival during a working vacation period,where the service rate of the customer is lower than a normal busy period.If the system is non-empty when the server returns from the working vacation,the server resumes the normal service period.Otherwise,the server will take successive working vacations till it reaches the maximum number of K working vacations and then the server remains idle until the next arrival.Closed-form probabilities are obtained by using the identities involving beta functions and degenerate hypergeometric functions,and the performance measures of the system are derived using generating functions.The stochastic decomposition structures of the mean queue length and mean waiting time are verified.The effects of the system parameters on some performance measures had been numerically illustrated.展开更多
We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digita...We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digital telecommunication systems and other related areas. For this queueing system, we present, based on Markov chain analysis, not only the steady-state distributions but also the transient distributions of the system length and of the system waiting time in a simple and unified manner. From these distributions, important performance measures of practical interest can be easily obtained. Numerical examples concerning the superposition of certain video traffics are presented at the end.展开更多
Semi-Markovian model of operation of a single-server queue system with losses and immediate service quality control has been built. In case of unsatisfactory request service quality, its re-servicing is carried out. R...Semi-Markovian model of operation of a single-server queue system with losses and immediate service quality control has been built. In case of unsatisfactory request service quality, its re-servicing is carried out. Re-servicing is executed till it is regarded satisfactory. Time between request income, and request service time are assumed to be random values with distribution functions of general kind. An explicit form of the system stationary characteristics has been defined.展开更多
We first consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process （BMAP）. The server serves customers in batches of maximum size ＇b＇ with a minimum thresh...We first consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process （BMAP）. The server serves customers in batches of maximum size ＇b＇ with a minimum threshold size ＇a＇. The service time of each batch follows general distribution independent of each other as well as the arrival process. The proposed analysis is based on the use of matrix-analytic procedure to obtain queue-length distribution at a post-departure epoch. Next we obtain queue-length distributions at various other epochs such as, pre-arrival, arbitrary and pre-service using relations with post-departure epoch. Later we also obtain the system-length distributions at post-departure and arbitrary epochs using queue-length distribution at post-departure epoch. Some important performance measures, like mean queue-lengths and mean waiting times have been obtained Total expected cost function per trait time is also derived to determine the locally optimal values of a and b. Secondly, we perform similar analysis for the corresponding infinite-buffer single server queue where arrivals occur according to a BMAP and service process in this case follows a non-renewal one, namely, Markovian service process （MSP）.展开更多
We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are investigated describing the b...We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are investigated describing the behavior of the system based on state space arrangements. The special features of the two formulations are discussed. The algorithms for calculating the stationary state probabilities are elaborated, based on which the main performance measures are obtained, and numerical examples are presented as well.展开更多
We consider an MX/M/c queue with catastrophes and state- dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, a...We consider an MX/M/c queue with catastrophes and state- dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these properties and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we obtain the Laplace transform of the transition probability for the absorbing MX/M/c queue.展开更多
In this paper, we consider a BMAP/G/1 G-queue with setup times and multiple vacations. Arrivals of positive customers and negative customers follow a batch Markovian arrival process （BMAP） and Markovian arrival proc...In this paper, we consider a BMAP/G/1 G-queue with setup times and multiple vacations. Arrivals of positive customers and negative customers follow a batch Markovian arrival process （BMAP） and Markovian arrival process （MAP） respectively. The arrival of a negative customer removes all the customers in the system when the server is working. The server leaves for a vacation as soon as the system empties and is allowed to take repeated （multiple） vacations. By using the supplementary variables method and the censoring technique, we obtain the queue length distributions. We also obtain the mean of the busy period based on the renewal theory.展开更多
文摘In this paper,we consider the impatient customers in M/M/1 queueing model under variant working vacation policy.The customer’s impatience is due to its arrival during a working vacation period,where the service rate of the customer is lower than a normal busy period.If the system is non-empty when the server returns from the working vacation,the server resumes the normal service period.Otherwise,the server will take successive working vacations till it reaches the maximum number of K working vacations and then the server remains idle until the next arrival.Closed-form probabilities are obtained by using the identities involving beta functions and degenerate hypergeometric functions,and the performance measures of the system are derived using generating functions.The stochastic decomposition structures of the mean queue length and mean waiting time are verified.The effects of the system parameters on some performance measures had been numerically illustrated.
文摘We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digital telecommunication systems and other related areas. For this queueing system, we present, based on Markov chain analysis, not only the steady-state distributions but also the transient distributions of the system length and of the system waiting time in a simple and unified manner. From these distributions, important performance measures of practical interest can be easily obtained. Numerical examples concerning the superposition of certain video traffics are presented at the end.
文摘Semi-Markovian model of operation of a single-server queue system with losses and immediate service quality control has been built. In case of unsatisfactory request service quality, its re-servicing is carried out. Re-servicing is executed till it is regarded satisfactory. Time between request income, and request service time are assumed to be random values with distribution functions of general kind. An explicit form of the system stationary characteristics has been defined.
基金partial financial support from the Department of Science and Technology,New Delhi,India under the research grant SR/FTP/MS-003/2012
文摘We first consider an infinite-buffer single server queue where arrivals occur according to a batch Markovian arrival process （BMAP）. The server serves customers in batches of maximum size ＇b＇ with a minimum threshold size ＇a＇. The service time of each batch follows general distribution independent of each other as well as the arrival process. The proposed analysis is based on the use of matrix-analytic procedure to obtain queue-length distribution at a post-departure epoch. Next we obtain queue-length distributions at various other epochs such as, pre-arrival, arbitrary and pre-service using relations with post-departure epoch. Later we also obtain the system-length distributions at post-departure and arbitrary epochs using queue-length distribution at post-departure epoch. Some important performance measures, like mean queue-lengths and mean waiting times have been obtained Total expected cost function per trait time is also derived to determine the locally optimal values of a and b. Secondly, we perform similar analysis for the corresponding infinite-buffer single server queue where arrivals occur according to a BMAP and service process in this case follows a non-renewal one, namely, Markovian service process （MSP）.
基金Supported by National Social Science Foundation of China(No.11BTJ011)Humanities and Social Sciences Foundation of Ministry of Education of China,2012(No.12YJAZH173)
文摘We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are investigated describing the behavior of the system based on state space arrangements. The special features of the two formulations are discussed. The algorithms for calculating the stationary state probabilities are elaborated, based on which the main performance measures are obtained, and numerical examples are presented as well.
基金This work was substantially supported by the National Natural Sciences Foundations of China （Grant Nos. 11371374, 11771452, 11701489, 11571372）, the National Natural Science Foundation of China-Tian Yuan （Grant No. 11626203）, and the Natural Sciences Foundations of Hunan Province （No. 2017JJ2328）.
文摘We consider an MX/M/c queue with catastrophes and state- dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these properties and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we obtain the Laplace transform of the transition probability for the absorbing MX/M/c queue.
基金supported by the National Natural Science Foundation of China (No. 10871064)
文摘In this paper, we consider a BMAP/G/1 G-queue with setup times and multiple vacations. Arrivals of positive customers and negative customers follow a batch Markovian arrival process （BMAP） and Markovian arrival process （MAP） respectively. The arrival of a negative customer removes all the customers in the system when the server is working. The server leaves for a vacation as soon as the system empties and is allowed to take repeated （multiple） vacations. By using the supplementary variables method and the censoring technique, we obtain the queue length distributions. We also obtain the mean of the busy period based on the renewal theory.
