Discrete-time Full Service Two Polling System Theory

In computer and communication network, for channel multiplexing and medium access control, there are two main ways:Polling and random access. Since the emergence of official modeling and analysis, polling systems have been widely used for traffic signal control, industrial control, manufacture and logistics, in particular, widely used in the field of computer and communication networks.The basic polling model consists of N queues, in which the server serves orderly each queue under the control of some rules. After serving the last queue, the server shifts to serve the first queue, which it repeats the same service order. Polling systems use this kind of control mode so that all users can non-competitively share system resources, for example, channel, bandwidth, central processing unit (CPU) in computers and communication network, and so on.The operation process of polling systems consists of customer arriving at every queue, the server serving customers in every queue and the server shifting from one queue to next queue.Based on the different service policies, polling systems can be classified into three types:Exhaustive, Gated and Limited-K.While studying the polling system, one of the important performance measures is mean queue length, namely queuing customers for service in a queue. Another important performance measure is mean customer waiting time, namely the time interval from a customer arriving at a queue to its departing from the queue.In addition, mean cycle time is alse one important performance measure, which is the time interval from the instant the server beginning to serve a queue to the instant the server beginning to serve again the same queue.In fact, while studing the polling system, the ultimate purpose is to obtain the close-formed expressions about the performance measures, by which designers can understand better the system, so improve and optimize the system efficiency.The basic polling system has been improved and optimized for the need of different application. The close-formed expressions for the basic polling system have beed obtained. But, for improved and optimized polling models, because of their analysis complexity and difficulty, many literatures either gave the approximate results by numerical analysis, or gave only the simulation results.This paper presents characteristics of three polling system which use different service policies, namely exhaustive, gated and limited (K = 1) service. The paper presents the new method using the embedded Markov chain (Markov Chain) and probability generating function to obtain the probability generating functions describing the states of the system, and presents the closed form expressions of the performance measures, namely mean queue length and mean waiting time.Exhaustive service polling systems characteristically have a shorter mean waiting time, which is especially important for applications that require systems with shorter mean waiting times. The paper proposes a discrete exhaustive polling model with two-level, which consists of one key queue h with higher priority and N ordinary queues with lower priorities. The exhaustive policy is used by all queues including both the key queue h and the N ordinary queues. Every time after orderly serving one of the ordinary queues, going through a switching time, the server shifts to serve the key queue. In the paper, embedded Markov chain and probability generating functions are applied to derive the generating functions describing system states. Based on the generating functions, we use the iterative method to resolve the first derivatives and second derivatives of generating functions, and then we obtain the closed-form expressions of the mean queue length and mean waiting time.Wireless sensor networks consist of many tiny smart sensor nodes. Besides one kind or many kinds of functions to sense environment variation, sensor nodes contain the processor and radios. Wireless sensor networks are self-organizing multi-hop ad hoc networks. Large scale wireless sensor networks have been applied in a variety of the field, such as medical monitoring, environmental monitoring, surveillance, home security, military operations, and industrial machine monitoring etc. In coming year, as advances have arisen in micro-fabrication technology, the cost of manufacturing sensor nodes continues to drop, and increasing deployments of wireless sensor networks are expected.Wireless sensor nodes are powered by the battery. It may be difficult to recharge the battery, or nodes themselves may be so cheap that recharging them may not be cost-effective. It is so important for wireless sensor networks to operate in energy-efficient to achieve the satisfactory network lifetime that energy efficiency should be tackled on the level of the entire network. One of the key aspects is organization of network communications as the radio is the main energy consumer in a sensor node. The only way to reduce this energy consumption is to completely turn their radio off. However, besides sensing environment variation, sensor nodes also need to form the ad hoc network to forward data to the data sink.Enabling wireless sensor networks to minimize energy loss in the monitoring state there are usually two main methods, the one is to design MAC protocols with periodic sleep/ wake scheduling mode, the second is to design hardware to real-time wake-up the sensor nodes. This paper proposed a scheme using low-power hardware circuits to monitor. Sensor nodes have two different channels, namely data channel and monitoring channel. In the network initialization, each node is assigned a different wake-up tone from its neighbors. Without the need for data communication, sensor nodes only open low-power monitoring channel. When the source node needs to transfer information packets, it first sends the target node's wake-up tone to the target node. When the target node detects this wake-up tone, it will immediately open the data channel to communicate with the source node. Wake-up tune is composed just by a pulse waveform, so its amplifiing circuit does not too care distortion, so its quiescent point can be relatively low. The wake-up tone signal is amplified, directly sended to the digital circuit to identify. So the monitoring channel is low power dissipation, and low complexity, low cost, short response time, so the monitoring scheme is suitable for wireless sensor networks to increase energy efficiency and to reduce response time.MAC (Medium Access Control) protocol for wireless sensor networks is another key technology. With distribution and sharing limited resources in wireless communications, wireless sensor networks constructed the underlying infrastructure of communication system.In wireless sensor networks, the number of sensor nodes is very large, and sensor nodes often collaborate. Wireless sensor networks typically use clustering algorithm to group a large number of sensor nodes into many clusters, which enables the dynamic self-organization network to be relatively fixed structure. So in the paper, the discrete exhaustive two-level polling system is applied to clustering wireless sensor networks. In a cluster, cluster head node is the ken queue, the other nodes are the ordinary queues. Under the control of the logical center, every time after one ordinary node is polled, going through a switching time, the system shifts to poll the cluster head node, which can guarantee the priority of the cluster head node. Theoretical analysis and experimental results show that the mean waiting time of the cluster head node can be largely reduced, which can balance the energe comsuming among the sensor nodes, and each of sensor node timely send information packets, then go to sleep, which can improve energy efficiency.