Rejoinder on: queueing models for the analysis of communication systems

In this rejoinder, we respond to the comments and questions of three discussants of our paper on queueing models for the analysis of communication systems. Our responses are structured around two main topics: discrete-time modeling and further extensions of the presented queueing analysis

Optimum cost analysis for an Geo/Geo/c/N feedback queue under synchronous working vacations and impatient customers

This paper concerns the cost optimisation analysis of a discrete-time finite-capacity multiserver queueing system with Bernoulli feedback, synchronous multiple and single working vacations, balking, and reneging during both busy and working vacation periods. A reneged customer can be retained in the system by employing certain persuasive mechanism for completion of service. Using recursive method, the explicit expressions for the stationary state probabilities are obtained. Various system performance measures are presented. Further, a cost model is formulated. Then, the optimization of the model is carried out using quadratic fit search method (QFSM). Finally, the impact of various system parameters on the performance measures of the queueing system is shown numerically.</p

Power series approximations for two-class generalized processor sharing systems

We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are nonempty, a customer of queue 1 is served with probability beta, and a customer of queue 2 is served with probability 1-beta. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating function U(z (1),z (2)) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary value problems. Then, we propose to use the same functional equation to obtain a power series for U(z (1),z (2)) in beta. The first coefficient of this power series corresponds to the priority case beta=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations for the mean stationary queue lengths are obtained from combining truncated power series and Pad, approximation

Optimization of renewal input (a, c, b) policy working vacation queue with change over time and bernoulli schedule vacation interruption

This paper presents a renewal input single working vacation queue with change over time and Bernoulli schedule vacation interruption under (a, c, b) policy. The service and vacation times are exponentially distributed. The server begins service if there are at least c units in the queue and the service takes place in batches with a minimum of size a and a maximum of size b (a ≤ c ≤ b). The change over period follows if there are (a − 1) customers at service completion instants. The steady state queue length distributions at arbitrary and pre-arrival epochs are obtained. An optimal cost policy is presented along with few numerical experiences. The genetic algorithm and quadratic fit search method are employed to search for optimal values of some important parameters of the system.Publisher's Versio

空間Webデータにおけるm-最近接キーワード検索問題のトップダウン解法に関する研究

This thesis addresses the problem of m-closest keywords queries (mCK queries) over spatial web objects that contain descriptive texts and spatial information. The mCK query is a problem to find the optimal set of records in the sense that they are the spatially-closest records that satisfy m user-given keywords in their texts. The mCK query can be widely used in various applications to find the place of user’s interest.　Generally, top-down search techniques using tree-style data structures are appropriate for finding optimal results of queries over spatial datasets. Thus in order to solve the mCK query problem, a previous study of NUS group assumed a specialized R*-tree (called bR*-tree) to store all records and proposed a top-down approach which uses an Apriori-based node-set enumeration in top-down process. However this assumption of prepared bR*-tree is not applicable to practical spatial web datasets, and the pruning ability of Apriori-based enumeration is highly dependent on the data distribution.　In this thesis, we do not expect any prepared data-partitioning, but assume that we create a grid partitioning from necessary data only when an mCK query is given. Under this assumption, we propose a new search strategy termed Diameter Candidate Check (DCC), which can find a smaller node-set at an earlier stage of search so that it can reduce search space more efficiently. According to DCC search strategy, we firstly employ an implementation of DCC strategy in a nested loop search algorithm (called DCC-NL). Next, we improve the DCC-NL in a recursive way (called RDCC). RDCC can afford a more reasonable priority order of node-set enumeration. We also uses a tight lower bound to improve pruning ability in RDCC.　RDCC performs well in a wide variey of data distributions, but it has still deficiency when one data-point has many query keywords and numerous node-sets are generated. Hence in order to avoid the generation of node-sets which is an unstable factor of search efficiency, we propose another different top-down search approach called Pairwise Expansion. Finally, we discuss some optimization techniques to enhance Pairwise Expansion approach. We first discuss the index structure in the Pairwise Expansion approach, and try to use an on-the-fly kd-tree to reduce building cost in the query process. Also a new lower bound and an upper bound are employed for more powerful pruning in Pairwise Expansion.　We evaluate these approaches by using both real datasets and synthetic datasets for different data distributions, including 1.6 million of Flickr photo data. The result shows that DCC strategy can provide more stable search performance than the Apriori-based approach. And the Pairwise Expansion approach enhanced with lower/upper bounds, has more advantages over those algorithms having node-set generation, and is applicable for real spatial web data.電気通信大学201

Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns

In this paper we consider a like-queue production system in which server startup and breakdowns are possible. The server is turned on (i.e. begins startup) when N units are accumulated in the system and off when the system is empty. We model this system by an M[x]/M/1 queue with server breakdowns and startup time under the N policy. The arrival rate varies according to the server's status: off, startup, busy, or breakdown. While the server is working, he is subject to breakdowns according to a Poisson process. When the server breaks down, he requires repair at a repair facility, where the repair time follows the negative exponential distribution. We study the steady-state behaviour of the system size distribution at stationary point of time as well as the queue size distribution at departure point of time and obtain some useful results. The total expected cost function per unit time is developed to determine the optimal operating policy at a minimum cost. This paper provides the minimum expected cost and the optimal operating policy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided

Queueing systems with periodic service

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Discrete-time queueing model for responsive network traffic and bottleneck queues

The Internet has been more and more intensively used in recent years. Although network infrastructure has been regularly upgraded, and the ability to manage heavy traffic greatly increased, especially on the core networks, congestion never ceases to appear, as the amount of traffic that flow on the Internet seems to be increasing at an even faster rate. Thus, congestion control mechanisms play a vital role in the functioning of the Internet. Active Queue Management (AQM) is a popular type of congestion control mechanism that is implemented on gateways (most notably routers), which can predict and avoid the congestion before it happens. When properly configured, AQMs can effectively reduce the congestion, and alleviate some of the problems such as global synchronisation and unfairness to bursty traffic. However, there are still many problems regarding AQMs. Most of the AQM schemes are quite sensitive to their parameters setting, and these parameters may be heavily dependent on the network traffic profile, which the administrator may not have intensive knowledge of, and is likely to change over time. When poorly configured, many AQMs perform no better than the basic drop-tail queue. There is currently no effective method to compare the performance of these AQM algorithms, caused by the parameter configuration problem. In this research, the aim is to propose a new analytical model, which mainly uses discrete-time queueing theory. A novel transient modification to the conventional equilibrium-based method is proposed, and it is utilised to further develop a dynamic interactive model of responsive traffic and bottleneck queues. Using step-by-step analysis, it represents the bursty traffic and oscillating queue length behaviour in practical network more accurately. It also provides an effective way of predicting the behaviour of a TCP-AQM system, allowing easier parameter optimisation for AQM schemes. Numerical solution using MATLAB and software simulation using NS-2 are used to extensively validate the proposed models, theories and conclusions