On M/G/1 system under NT policies with breakdowns, startup and closedown

AbstractThis paper studies the vacation policies of an M/G/1 queueing system with server breakdowns, startup and closedown times, in which the length of the vacation period is controlled either by the number of arrivals during the vacation period, or by a timer. After all the customers are served in the queue exhaustively, the server is shutdown (deactivates) by a closedown time. At the end of the shutdown time, the server immediately takes a vacation and operates two different policies: (i) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or the waiting time of the leading customer reaches T units; and (ii) The server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time units have elapsed since the end of the closedown time. If the timer expires or the number of arrivals exceeds the threshold N, then the server reactivates and requires a startup time before providing the service until the system is empty. If some customers arrive during this closedown time, the service is immediately started without leaving for a vacation and without a startup time. We analyze the system characteristics for each scheme

Impatient Customers in an Markovian Queue with Bernoulli Schedule Working Vacation Interruption and Setup Time

In this paper, using probability generating function method, Impatient customers in an Markovian queue with Bernoulli schedule working vacation interruption and setup time is discussed. Customers impatience is due to the servers vacation. During the working vacation period, if there are customers in the queue, the vacation can be interrupted at a service completion instant and the server begins a regular service period with probability (1 - b) or continues the vacation with probability b. We obtain the probability generating functions of the stationary state probabilities, performance measures, sojourn time of a customer and stochastic decomposition of the queue length, waiting time and numerical results

Performance of the IEEE 802.16e sleep mode mechanism in the presence of bidirectional traffic

We refine existing performance studies of the WiMAX sleep mode operation to take into account uplink as well as downlink traffic. This as opposed to previous studies which neglected the influence of uplink traffic. We obtain numerically efficient procedures to compute both delay and energy efficiency characteristics. A test scenario with an Individual Subscriber Internet traffic model in both directions shows that even a small amount of uplink traffic has a profound effect on the system performance

A pseudoconservation law for a time-limited service polling system with structured batch poisson arrivals

AbstractWe consider a cyclic-service queueing system (polling system) with time-limited service, in which the length of a service period for each queue is controlled by a timer, i.e., the server serves customers until the timer expires or the queue becomes empty, whichever occurs first, and then proceeds to the next queue. The customer whose service is interrupted due to the timer expiration is attended according to the nonpreemptive service discipline. For the cyclic-service system with structured batch Poisson arrivals (Mx/G/1) and an exponential timer, we derive a pseudoconservation law and an exact mean waiting time formula for the symmetric system

On a Multiserver Queueing System with Customers’ Impatience Until the End of Service Under Single and Multiple Vacation Policies

This paper deals with a multiserver queueing system with Bernoulli feedback and impatient customers (balking and reneging) under synchronous multiple and single vacation policies. Reneged customers may be retained in the system. Using probability generating functions (PGFs) technique, we formally obtain the steady-state solution of the proposed queueing system. Further, important performance measures and cost model are derived. Finally, numerical examples are presented

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

Analysis of queueing models with batch service

This dissertation is the result of my research work at the SMACS research group (Department of Telecommunications and Information Processing, Ghent University) and it concerns the analysis of queueing models with batch service. A queueing model basically is a mathematical abstraction of a situation where customers arrive and queue up until they receive some kind of service. These phenomena are omnipresent in real life: people waiting at a counter of a post office or bank, people in the waiting room of a doctor, airplanes waiting to take off, people waiting until they get connected with the call center, data packets which are temporarily stored into a buffer until the transmisssion channel is available, et cetera. The analysis of queueing models constitutes the subject of the applied mathematical discipline called queueing theory and amounts to answering questions such as “How many customers are waiting on average?”, “How long do customers have to wait?”, “Is there a large variation on the waiting time?”, “What is the probability that data packets are lost due to a full buffer?”, “What is the probability that a customer suffers a lengthy delay?”, et cetera. In queueing theory, the number of customers and their waiting time are often denominated by respectively buffer content and customer delay. In addition, the probability that a quantity, such as the buffer content or customer delay, is very large or lengthy, is generally called a tail probability. The models we investigate throughout this dissertation have in common that customers can be served in batches, meaning that several customers can be served simultaneously. An elevator can be viewed as a classic example, as several people can be transported simultaneously to another floor. Also, in a variety of production or transport processes several goods can be processed together. Furthermore, in quality control, classification of items as good or bad can often be achieved more economically by examining the items in groups rather than individually. If the result of a group test is good, all items within it can then be classified as good, whereas one or more items are bad in the opposite case, where the items can then be retested by considering smaller groups. Group testing is especially of importance when the percentage of bad items is small. In addition, in telecommunications networks, packets with the same destination and quality of service (QoS) requirements are often aggregated into so-called bursts and these bursts are transmitted over the network. This is mainly done for efficiency reasons, since only one header per aggregated burst has to be constructed, instead of one header per single information unit, thus leading to an increased throughput. Technologies using packet aggregation include for instance Optical burst switched (OBS) networks and IEEE 802.11n wireless local area networks (WLANs). An inherent aspect of batch service is that newly arriving customers cannot join the ongoing service, even if there is free capacity (we denominate the maximum number of customers that can be served simultaneously by server capacity). For instance, an arriving person cannot enter an elevator that has just left, even if space is available. This person has to wait until the elevator has transported its occupants to their requested floors and has returned, which might take a long time in high buildings. In view of this, it is of importance to take a well-considered decision when the server becomes available and finds less customers than it can serve in theory. This decision is called the service policy. A whole spectrum of service policies exist. The server could, for instance, start serving the already present customers immediately. Although the present customers benefit from this approach, capacity is wasted: customers that arrive later cannot join the ongoing service. An alternative for this so-called immediate-batch service policy is the full-batch service policy. In this case, the available server postpones service until the number of present customers reaches or exceeds the server capacity, which, in turn, has a negative effect on the delay of the customers waiting to form a full batch (postponing delay). The threshold-based policy is a kind of compromise between immediate-batch service policy and full-batch service policy. When the number of present customers is below some service threshold, service is postponed, whereas service is initiated when the number of present customers reaches or exceeds this threshold. It is important to realize that even with this compromise, long postponing delays are possible. Therefore, in this dissertation, we combine a thresholdbased policy with a timer mechanism that avoids excessive postponing delays. The purpose of this dissertation is to calculate a large spectrum of performance measures, which enable to evaluate a broad set of situations with batch service and aid in selecting an efficient service policy. The studied performance measures are moments, such as the mean value and variance, and tail probabilities of the buffer content and the customer delay. This dissertation is structured as follows. In chapter 1, we motivate our work and we introduce crucial concepts such as probability generating functions (PGFs), whose useful properties are frequently relied upon throughout the analysis. Then we deduce moments and tail probabilities of the buffer content in chapter 2. The resulting formulas still contain unknown probabilities that have to be calculated numerically. As this might become unfeasible in some cases, we compute in chapter 3 approximations for the buffer content. Next, moments and tail probabilities of the customer delay are covered in respectively chapters 4 and 5. In order to analyze the moments, we conceive the customer delay as the sum of two non-overlapping parts, whereas for the tail probabilities, it turns out to be more convenient to interpret the delay as the maximum of two time periods. Further, in real life the customer arrival process often exhibits some kind of dependency. For instance, if a large amount of customers have recently arrived, it is likely that many customers arrive in the near future, as it might be an indication of a peak moment. Therefore, we investigate in chapter 6 the influence of dependency in the arrival process on the behaviour of batch-service phenomena and on the selection of an efficient service policy. Finally, the main contributions are summarized in chapter 7

Energy saving policies for a machine tool with warm-up, stochastic arrivals and buffer information

One of the measures for saving energy in manufacturing is the implementation of control strategies that reduces energy consumption during the machine idle periods. Specifically, the paper proposes a framework that integrates different control policies for switching the machine off when the production is not critical, and on either when the part flow has to be resumed or the queue has accumulated to a certain level. A general policy is formalized by modeling explicitly the power consumed in each machine state. A threshold policy is analyzed and the optimal parameter is provided for an M/M/1/K system. Numerical results are based on data acquired with dedicated experimental measurements on a real machining centre, and a comparison with common practices in manufacturing is also reported