Optimization of polling systems with Bernoulli schedules

Optimization;Polling Systems;Queueing Theory;operations research

Analysis of a M/M/c queue with single and multiple synchronous working vacations

We consider a M/M/c queuing system with synchronous working vacation and two different policies of working vacation i.e. a multiple working vacation policy and a single working policy. During a working vacation the server does not completely halts the service rather than it will render service at a lower rate. In synchronous vacation policy all the servers leave for a vacation simultaneously, when the server finds the system empty after finishing serving a customer. In multiple working vacation (MWV) policy the servers continue to take vacation till they find the system nonempty at a vacation completion instant. Single working vacation (SWV) policy is different from the multiple working vacation policy in a way that, when the working vacation ends and servers find the system empty, they remains idle until the first arrival occurs rather than taking another vacation. We have derived explicit expressions for some performance measures in terms of two indexes by using PGF method. We derived some results regarding the limiting behavior of some performance measures based on these two indexes. A comparison between the models is carried out and numerical results are provided to illustrate the effects of various parameters on system performance measures

Energy-saving policies for temperature-controlled production systems with state-dependent setup times and costs

There are numerous practical examples of production systems with servers that require heating in order to process jobs. Such production systems may realize considerable energy savings by temporarily switching off the heater and building up a queue of jobs to be processed later, at the expense of extra queueing costs. In this paper, we optimize this trade-off between energy and queueing costs. We model the production system as an M/G/1 queue with a temperature-controlled server that can only process jobs if a minimum production temperature is satisfied. The time and energy required to heat a server depend on its current temperature, hence the setup times and setup costs for starting production are state dependent. We derive the optimal policy structure for a fluid queue approximation, called a wait-heat-clear policy. Building upon these insights, for the M/G/1 queue we derive exact and approximate costs for various intuitive types of wait-heat-clear policies. Numerical results indicate that the optimal wait-heat-clear policy yields average cost savings of over 40% compared to always keeping the server at the minimum production temperature. Furthermore, an encouraging result for practice is that simple heuristics, depending on the queue length only, have near-optimal performance

Impact of N-Policy on Quality of Service for Energy Efficient Wireless Sensor Networks

Wireless Sensor Networks (WSNs) have attracted attention from both academia and industry since the late 90\u27s. Recent advancements in the technology of microelectromechanical systems (MEMS), the fields of digital electronics, and in wireless communication have resulted in the reductions of both the size and cost of sensor nodes. Even so, there are still some constraints on the performance of WSNs. The two most important constraints are the limited power supply in the sensor nodes and the difficulty in recharging or replacing their batteries. Therefore, reducing the energy consumption of Pensor nodes and optimizing the lifetime of WSNs are crucial. Wireless sensor networks have explored many new protocols, various approaches have been taken to design energy-efficient wireless sensor networks (EEWSNs). In this work, we conducted research on a packet queueing management model that offers different quality of services for packets coming from different sources. This model also incorporate N-policy to minimize excessive switching of transmission radio to conserve battery energy. In our daily life, we often experience waiting in a queue to receive some kind of service. Some customers do not join the queue at the end like other normal customers, and try to cut in the queue hoping to have a shorter waiting time and a higher level of satisfaction. This behavior is called customer interjection. First-come- first-served (FCFS) service discipline is usually assumed in public places like restaurants, banks, airports, and supermarkets. However, customer interjections can still be seen in these places. These interjections can affect the waiting time of other customers in queue. Such interjections may reduce the waiting time of interjecting customers, but increase the waiting time and of others. To control a queueing system, implementing a priority mechanism is a sensible approach. For example, at the airport, customers are categorized in to VIP and general customers. VIP customer has shorter lines and tailored services where as general customer usually stand in line longer and process takes longer to finish too. Priority queue management becomes more important in telecommunication systems also in computer systems (e.g. operating systems) they have been exploited for a long time. Priority queueing control is also used in other production practices. In this research we proposed a queue management model that has a priority queue and a normal queue at the same time. Our proposed model will service priority packets first then turn around to process normal packet until both queues are empty then turn off the radio. This seemingly simple design yields a complex set of balance equations. After solving all the equations with the help of probability generating functions we got the expected queue length for two queues

Inventory control in multi-item production systems

This thesis focusses on the analysis and construction of control policies in multiitem production systems. In such systems, multiple items can be made to stock, but they have to share the finite capacity of a single machine. This machine can only produce one unit at a time and if it is set-up for one item, a switch-over or set-up time is needed to start the production of another item. Customers arrive to the system according to (compound) Poisson processes and if they see no stock upon arrival, they are either considered as a lost sale or backlogged. In this thesis, we look at production systems with backlog and production systems with lost sales. In production systems with lost sales, all arriving customers are considered lost if no stock is available and penalty costs are paid per lost customer. In production systems with backlog, arriving customers form a queue if they see no stock and backlogging costs are paid for every backlogged customer per time unit. These production systems find many applications in industry, for instance glass and paper production or bulk production of beers, see Anupindi and Tayur [2]. The objective for the production manager is to minimize the sum of the holding and penalty or backlogging costs. At each decision moment, the manager has to decide whether to switch to another product type, to produce another unit of the type that is set-up or to idle the machine. In order to minimize the total costs, a balance must be found between a fast switching scheme that is able to react to sudden changes in demand and a production plan with a little loss of capacity. Unfortunately, a fast switching scheme results in a loss of capacity, because switching from one product type to another requires a switch-over or set-up time. In the optimal production strategy, decisions depend on the complete state of the system. Because the processes at the different product flows depend on these decisions, the processes also depend on the complete state of the system. This means that the processes at the different product flows are not independent, which makes the analysis and construction of the optimal production strategy very complex. In fact, the complexity of the determination of this policy grows exponentially in the number of product types and if this number is too large, the optimal policy becomes intractable. Production strategies in which decisions depend on the complete system are defined as global lot sizing policies and are often difficult to construct or analyse, because of the dependence between the different product flows. However, in this thesis the construction of a global lot sizing policy is presented which also works for production systems with a large number of product types. The key factor that makes the construction possible is the fact that it is based on a fixed cycle policy. In Chapter 2, the fixed cycle policy is analysed for production systems with lost sales and in Chapter 6, the fixed cycle policy is analysed for production systems with backlog. The fixed cycle policy can be analysed per product flow and this decomposition property allows for the determination of the so called relative values. If it is assumed that one continues with a fixed cycle control, the relative values per product type represent the relative expected future costs for each decision. Based on these relative values, an improvement step (see Norman [65]) is performed which results in a ‘one step improvement’ policy. This policy is constructed and analysed in Chapters 2 and 7 for production systems with lost sales and production systems with backlog, respectively. This global lot sizing policy turns out to perform well compared to other, heuristic production strategies, especially in systems with a high load and demand processes with a high variability. A similar approach as for the production system with a single machine is performed in a system with two machines and lost sales in Chapter 3. Results show that in some cases the constructed strategy works well, although in some systems two separate one step improvement policies perform better. Examples of more heuristic production strategies are gated and exhaustive basestock policies. In these ’local lot sizing‘ policies, decisions depend only on the stock level of the product type that is set-up. But even in these policies, the processes at the different product flows are dependent. This makes the analysis difficult, but for production systems with backlog a translation can be made to a queueing system by looking at the number of products short to the base-stock level. So the machine becomes a server and each product flow becomes a queue. In these queueing systems, also known as polling systems, gated and exhaustive base-stock policies become gated and exhaustive visit disciplines. For polling systems, an exact analysis of the queue length or waiting time distribution is often possible via generating functions or Laplace-Stieltjes transforms. In Chapter 5, the determination of the sojourn time distribution of customers in a polling system with a (globally) gated visit discipline is presented, which comes down to the determination of the lead time distribution in the corresponding production system