• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.157-172
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• 2004

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival of all the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using the regeneration point technique. The mean number of cells which die in time t and its asymptotic behaviour are discussed. When the disasters arrival as a Poisson process and the lifetime of the cells follows exponential distribution, elegant inter- relationships are found among the means of (i) the total number of cells which die in time t (ii) the total sojourn time of all cells in the system upto time t and (iii) the number of living cells at time t. Some of the existing results are deduced as special cases for related processes.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.405-434
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• 1998

We consider an M/M/c queue with two types of custormers, positive customers and negative customers. Positive customers are ordinary ones who upon arrival, join a queue with the intention of getting served and each arrival of negative customer removes a positive customer in the system, if any presents, and then is disappeared immediately. The Laplace-Stieltjes transforms (LST's) of the sojourn time distributions of a tagged customer, joinly with the probability that the tagged customer completes his service without being removed are derived under the combinations of various service displines; FCFS, LCFS and PS and removal strategies; RCF, RCH and RCR.

• Journal of Korea Society of Industrial Information Systems
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• v.29 no.1
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• pp.63-76
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• 2024

In this study, we analyzed queue length and sojourn time of discrete-time BMAP/G/1 queues under the workload control. Group customers (packets) with correlations arrive at the system following a discrete-time Markovian arrival process. The server starts busy period when the total service time of the arrived customers exceeds a predetermined workload threshold D and serves customers until the system is empty. From the analysis of workload and waiting time, distributions of queue length at the departure epoch and arbitrary time epoch and system sojourn time are derived. We also derived the mean value as a performance measure. Through numerical examples, we confirmed that we can obtain results represented by complex forms of equations, and we verified the validity of the theoretical values by comparing them with simulation results. From the results, we can obtain key performance measures of complex systems that operate similarly in various industrial fields and to analyze various optimization problems.

• Communications for Statistical Applications and Methods
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• v.25 no.4
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• pp.443-451
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• 2018

$P^M_{\lambda}$-service policy is a workload dependent hysteretic policy. The policy has two service states comprised of the ordinary stage and the fast stage. An ordinary service stage is initiated by the arrival of a customer in an idle state. When the workload of the server surpasses threshold ${\lambda}$, the ordinary service stage changes to the fast service state, and it continues until the system is empty. These service stages alternate in this manner. When the cost of changing service stages is high, the hysteretic policy is more efficient than the threshold policy, where a service stage changes immediately into the other service stage at either case of the workload's surpassing or crossing down a threshold. $P^M_{\lambda}$-service policy is a modification of $P^M_{\lambda}$-policy proposed to control finite dams, and also an extension of the well-known D-policy. The distributions of the stationary workload of $P^M_{\lambda}$-service policy and its variants are studied well. However, there is no known result on the sojourn time distribution. We prove that there is a relation between the sojourn time of a customer and the first up-crossing time of the workload process over the threshold ${\lambda}$ after the arrival of the customer. Using the relation and the duality of M/G/1 and G/M/1 queues, we obtain conditional sojourn time distributions in M/G/1 and G/M/1 queues under the policy.

• ETRI Journal
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• v.25 no.4
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• pp.238-246
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• 2003

This paper introduces the modeling and analysis of a discrete-time, two-phase queueing system for both exhaustive batch service and gated batch service. Packets arrive at the system according to a Bernoulli process and receive batch service in the first phase and individual services in the second phase. We derive the probability generating function (PGF) of the system size and show that it is decomposed into two PGFs, one of which is the PGF of the system size in the standard discrete-time Geo/G/1 queue without vacations. We also present the PGF of the sojourn time. Based on these PGFs, we present useful performance measures, such as the mean number of packets in the system and the mean sojourn time of a packet.

• Management Science and Financial Engineering
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• v.2 no.1
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• pp.123-145
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• 1996

We consider a priority-based multiclass queue with probabilistic feed-back. There are J service stations. Each customer belongs to one of the several priority classes, and the customers of each class arrive at each station in a Poisson process. A single server serves queued customers on a priority basis with a nonpreemptive scheduling discipline. The customers who complete their services feed back to the system instantaneously and join one of the queues of the stations or depart from the system according to a given probability. In this paper, we propose a new method to simplify the analysis of these queueing systems. By the analysis of busy periods and regenerative processes, we clarify the underlying system structure, and systematically obtain the mean for the sojourn time, i.e., the time from the arrival to the departure from the system, of a customer at every station. The mean for the number of customers queued in each station at an arbitrary time is also obtained simultaneously.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.8 no.2
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• pp.100-107
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• 2009

Velocity estimation is one of important issues for efficient system management in mobile cellular systems. In this paper, a modified velocity estimation scheme which works in Adaptive Antenna System (AAS) is proposed. The proposed scheme estimates user velocity based on moving distance information and sojourn time information. From numerical results, it is shown that the proposed scheme can estimate user velocity accurately with low cost.

• ETRI Journal
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• v.36 no.4
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• pp.609-616
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• 2014

Even though many computational methods (recursive formulae) for blocking probabilities in finite-capacity M/D/1 queues have already been produced, these are forms of transforms or are limited to single-node queues. Using a distinctly different approach from the usual queueing theory, this study introduces explicit (transform-free) formulae for a blocking probability, a stationary probability, and mean sojourn time under either production or communication blocking policy. Additionally, the smallest buffer capacity subject to a given blocking probability can be determined numerically from these formulae. With proper selection of the overall offered load ${\rho}$, the approach described herein can be applicable to more general queues from a computational point of view if the explicit expressions of random vector $D_n$ are available.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.2
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• pp.1-12
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• 1997

We consider an M/M/2 queue with two servers placed in series. System performance measures that we present in closed expressions are the first and the second moments for the system size, the queue walting time and the sojourn time. We also present an algorithm for computing the queue waiting time distribution function based on the randomization method. As an application, we analyze the double tollbooth system and compare its performance with the conventional single tollbooth system's.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.4
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• pp.895-909
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• 2013

Distributed Denial-of-Service (DDoS) attacks towards name servers of the Domain Name System (DNS) have threaten to disrupt this critical service. This paper studies the vulnerability of the cache server to the flooding DNS query traffic. As the resolution service provided by cache server, the incoming DNS requests, even the massive attacking traffic, are maintained in the waiting queue. The sojourn of requests lasts until the corresponding responses are returned from the authoritative server or time out. The victim cache server is thus overloaded by the pounding traffic and thereafter goes down. The impact of such attacks is analyzed via the model of queuing process in both cache server and authoritative server. Some specific limits hold for this practical dual queuing process, such as the limited sojourn time in the queue of cache server and the independence of the two queuing processes. The analytical results are presented to evaluate the impact of DDoS attacks on cache server. Finally, numerical results are provided for further analysis.