A Wireless Sensor Networks

Published Date: 02 Nov 2017

A wireless sensor network, abbreviated as WSN, consists of a possibly large number of wireless devices able to take environmental measurements such as temperature, light, sound and humidity. With the development of the technology, the wireless devices even can sense the video and audio and transmit it. These sensor readings are transmitted over a wireless channel to a running application that makes decisions based on these sensor readings. It is described in the section that some examples of proposed wireless sensor applications and consider the following questions to motivate and an application-based viewpoint:

\item What is the trend of WSN's applications like?

The one recognized issue is the limited power available to each wireless sensor node, but there are other challenges such as the limited processing and the data backbone problems.

\item What are the requirements of the applications to the wireless sensor networks?

There are already some proposed publications of the traditional wireless sensor network's applications which will be introduced in the following parts. But with the development of the technologies and the higher requirements of the human beings, the more and more applications with new type, new services and new requirements come out recently. As the result, the new requirements are analyzed.

\item Is there any solution to solve the problems of the new requirements?

Based on the new requirements that given by the current or future applications to the wireless sensor networks, it is necessary to find out a solution.

\item Is there a method can measure or evaluate the applications' performance with the new solution?

A sensor network is composed of a large number of sensor nodes, which are densely deployed either inside the phenomenon or very close to it\cite{WSNintr1}\cite{WSNintr2}. Generally, the position of each sensor node in the WSN need not be engineered or predetermined, which means it allows WSN has random deployment in inaccessible terrains or disaster relief operations. Also as the result of it, the WSN's protocols and algorithms must possess self-organizing capabilities. Another feature of WSN is the cooperative effort of sensor nodes. The sensor nodes are fitted with an onboard processor and they use their processing abilities to locally carry out computations and transmit only the required and partially processed data. Furthermore, WSN has some other features which may important:

\begin{itemize}

\item The sensor nodes are limited in power, computation capacities and memory;

\item The sensor nodes are densely deployed;

\item The sensor nodes are prone to failures;

\item The topology of a WSN changes very frequently;

\item The sensor nodes may not have global identification because of the large amount of overhead and large number of sensors.

\end{itemize}

Generally the sensor nodes' architecture in WSN is as Fig.\ref{f:node} shows \cite{WSNintr4app}.

A sensor nodes may be composed of several basic components which including a sensing unit, a processing unit, a communication subsystem, a coordination subsystem, a storage unit and an optional mobility/ actuation unit:

\begin{itemize}

\item The sensing units are usually composed with two subunits: sensors and analog-to digital-converters (ADCs). The analog signals produced by the sensors based on the observed phenomenon are converted into digital signals by the ADC and then fed into the processing unit. The traditional sensors are usually those ones which sense the temperature, humidity, acceleration and some other scalar data. Currently, the with the human beings' higher requirements to the WSN applications, the sensors begin to contain the camera and audio \textit{etc}.

\item The processing unit executes the system software in charge of coordinating sensing and communication tasks and it is interfaced with a storage unit.

\item The communication subsystem interfaces the device to the network and is composed of a transceiver unit and of communication software which usually includes a communication protocol stack and system software such as middleware, operating systems and virtual machines.

\item The coordination subsystem takes the charge of coordinating the operation of different network devices by performing operations such as network synchronization and location management.

\item The optional mobility/ actuation unit can enable movement or manipulation of objects.

\item The power unit is the most important part that powered the whole system and may supported by an energy scavenging unit such as solar cells or others.

\end{itemize}

\subsubsection{Network Layers}

As introduced in Ref.\cite{WSNintr1}, the protocol stack used by WSN is shown in Fig.\ref{f:layers}. This one combines power and routing awareness, integrates data with networking protocol, communicates power effciently through the wireless medium, and promotes cooperative efforts of WSN \cite{WSNintr1}. The layers of WSN are composed of physical layer, data link layer, network layer, transport layer and application layer and have power management plane, mobility management plane and task management plane.

\begin{itemize}

\item Physical layer: it addressed the needs of simple but robust modulation, transmission and receiving techniques.

\item Data link layer: in it a medium access control (MAC) protocol is needed and because of the noisy environment and the mobility, possible feature of the sensor nodes, it must be power-aware and able to minimize collision with neighbour's broadcasts.

\item Network layer: it focuses on the routing the data supplied by the transport layer.

\item Transport layer: it helps to maintain the flow of data if the application of WSN requires it.

\item Application layer: different types of applications software can be built and used on this layer, depending on the sensing tasks.

\item Power management plane: it takes the charge of managing how a sensor nodes uses its power, such as the sensor node may turn off its receiver or even sensor power after receiving a message from a neighbour node or just sensed a data from the environment. This can avoid getting duplicated messages which have less utility.

\item Mobility management plane: it detects and registers the movement of sensor nodes, so a route back to the user is always maintained and the sensor nodes can keep track of who are the neighbours of them. And by knowing it, they can balance their power and task usage. Note that not all the WSN applications allow the nodes to move. But with the higher requirements of the applications, the WSN applications with movable nodes comes out more and more currently.

\item Task management plane: it takes the responsibilities of banlancing and scheduling the sensing tasks. Not all the sensor nodes in WSN are required to perform the sensing task at the same time. As the result of it, soe sensor nodes perform the task more than the others depending on their power level or some other factors. This plane is needed so that the sensor nodes in WSN can work together in a more power-saving way and share resources between the sensor nodes.

\end{itemize}

For its convenience and inexpensive cost of collecting data, recently we have seen tremendous growth in the research and the application of various wireless sensor network (WSN) (e.g. wireless sensor network for military, for industry even underwater wireless sensor network, video wireless sensor network etc.). The growing applications give more bandwidth-intensive services and demand for larger bandwidth supplication from the backbone of the access network. Also more application requires the data to transmit through the network with a longer distance to realize the remote surveillance which is not realistic to achieve only by wireless transmission (one of the important reason is the huge energy consumption\cite{WSNintr3_LEACH}). The proposed applications and the trend of future applications is introduced in the following part and also the requirements are analyzed.

\subsection{Applications}

\subsubsection{Applications}

The applications of wireless sensor network have been applied in many areas for its great potential and they can be classified generally into the following categories.\cite{WSNintr2}\cite{WSNintr4app}

\begin{itemize}

\item Military. The WSN is developed from the military research and application. It is very potential in the applications like tactical surveillance\cite{WSNapp1} (land, sea), tracking troop movement (both sides), making ubiquitous and undetected smart mines, battlefield communication\cite{WSNapp2}, detection of hazardous agents\cite{WSNapp3}\cite{WSNapp4} (explosive, nuclear, biological, poisonous, radioactive) and environmental awareness (terrain mapping) etc.

\item Surveillance. Video and audio sensors are more and more used to enhance and complement existing surveillance systems against crime and terrorist attacks. In Ref.\cite{WSNapp5}, problems related to the transport of an audio signal through a wireless channel and sensor nodes are analyzed and a project for an audio surveillance system is presented. In most all the other applications introduced in this part also use the multimedia sensor as the monitor to 'feel' the world: locating missing persons, criminals or terrorists, inferring and recording potentially relevant activities such as thefts, car accidents, traffic violations, and other smart home surveillance\cite{WSNapp6}. Furthermore an application was developed in Ref.\cite{WSNapp7} which used the sensor network (that consists of 21 mobile nodes, 29 reference nodes, and one gateway) to track 21 medical assets so that the nurses can use more times to take care of patients and the patients can receive better medical services. Ref.\cite{WSNapp22} studied how to use WSN to satisfied the requirements of protection of critical infrastructures. And an innovative solution for ship intrusion detection was proposed in Ref.\cite{WSNapp23}.

\item Traffic Monitoring. It will be possible to monitor car traffic in big cities or on highways and deploy services that offer traffic routing advice to avoid congestion or identify violations\cite{WSNapp24}. In Ref.\cite{WSNapp8} the researchers proposed a smart parking advice systems based on WMSNs to detect available parking spaces and provide drivers with automated parking advice. Some other researchers considered realize traffic surveillance using video camera sensors\cite{WSNapp9}. Ref.\cite{WSNapp10} focuses on congestion control but while previous works considered scalar sensor nodes which only report events in the size of a few bytes, they addressed congestion control for information-intensive flows such as video flows for surveillance applications in pervasive wireless multimedia sensor networks.

\item Advanced Health Care. Wireless sensor network can be used to monitor and study the behaviour of elderly people as a means to identify the causes of illnesses that affect them like the research in Ref.\cite{WSNapp11} to monitor the patients suffering from dementia. Ref.\cite{WSNapp12} developed a prototype for remote health monitoring, and a four-levels hierarchical wireless body sensor network (WBSN) system is designed for biometrics and healthcare applications in Ref.\cite{WSNapp13}. Ref.\cite{WSNapp14}\cite{WSNapp20}\cite{WSNapp21} gives the description and experimental analysis of the application which is based on the main idea of using simple distributed sensor nodes in a home environment, to provide home assistants, nurses, healthcare centres and relatives with a degree of "understanding" and information about the actual persons health and activity status in order to fast determine what kind of help is needed. And Ref.\cite{WSNapp25} tried to avoid the congestions between the sensor nodes.

\item Gaming. Networked gaming is emerging as a popular recreational activity. WMSN can help to find applications in future prototypes that enhance the effect of the game environment on the game player\cite{WSNapp15}.

\item Environmental and Industrial. Wireless sensor network, especially wireless multimedia sensor networks can be used for time-critical, industrial, process control. Some projects and testbeds have be developed: Arrays of video sensors are used by oceanographers to determine the evolution of sandbars via image processing techniques\cite{WSNapp16}; Algorithm is designed for reliable video transmission within mine tunnel to enhance the reliability of the end-to-end monitoring of mine tunnel\cite{WSNapp17}; some researches focused on the environmental and structural monitoring such as structural health monitoring of bridges or buildings\cite{WSNapp18}; and some ones aiming at tracking the pollutions using underwater wireless sensor network\cite{WSNapp19} in the harbours. Ref.\cite{WSNapp26} proposed a solution to the remote mine tunnel monitoring challenge of its multipath and diffraction effect due to unreliable channel and limited capacity.

\end{itemize}

\subsubsection{The trend and requirements}

As introduced above, in recent years, the growing interest in the wireless sensor network has resulted in thousands of new applications \cite{WSNintr2}\cite{WSNintr4app}\cite{WSNintr10} that not only measured the scalar data from physical phenomena such as temperature, pressure, humidity or location of objects, but more aimed at revisiting the real world with the description of multimedia content, for example, audio and video streams and still images. Because of the new methods of collecting data, there are also many new challenges to the wireless sensor network.

With the trends of increasing number of various applications which come out with the developing of the wireless sensor network, the challenges become more obvious when designing the wireless sensor network and guaranteeing it applications quality of service.

\begin{itemize}

\item Larger deployed area vs. network's lifetime

The trends of application need the network to be deployed in lager areas to monitor the physical world. But it means the sensor nodes have to send their data through a long distance to the sink and the increasing consumption is unavoidable even it sends the data by multi-hops. With the increasing energy consumption level, the lifetime becomes shorter and shorter definitely. When the lifetime decreases to some extent, the whole network is useless and the application is failed.

\item Remote surveillance application vs. network's lifetime, data security and QoS

In some other conditions, the application only requires to surveillance an appropriate area for wireless sensor network but it need to transmit the data to some other place which is very far away from the surveillance area (such as monitoring the nuclear pollution, the volcanoes, forests fire etc. ). It is also impossible for sensor nodes to send the service data through the distance like this even it can send by the multi-hops. Especially for this type of applications it is hard or unexpected to recharge the nodes battery and it is usually expected to deploy just once. Therefore the saving energy and prolong the lifetime is the most significant to guarantee the application is working. In the other hands, the long distance wireless transmission always has company with high packet's loss rate and lower security level.

\item Delay sensitive application vs. one-sink structure

As the sensor density increases to infinity and more sensors send data especially multimedia data to the central controller. Most of the application chooses the sensor nodes to transmit using the CSMA/CD. But with the increasing amount of sensor nodes and the larger packet size of multimedia service, the occupancy rate of the wireless change is also increasing, which means the services' data have to wait for a longer time to access into the channel and the transmission delay will have a huge increase. For some delay sensitive applications (such as the ones for military, the ones with audio services etc.), it is unacceptable.

\item Bandwidth requirements vs. sink’s constant capacity

With more multimedia sensors are used in the applications, the bandwidth requirements to the sink in the wireless sensor network also became a big challenge. The applications of wireless sensor network trends to using the event driven algorithms to save more energy and make the network more effective which makes the requirement to the sink in the network is different. For the sink in the wireless sensor network, if it has a large capacity then it is a kind of waste when the event does not happen; on the contrary, if it has a small capacity it cannot fulfil the requirements of the bandwidth to transmit enough service packets.

\item Other challenges

There are challenges also face the wireless sensor networks when it is used in more application.

\end{itemize}

Therefore our research aims at solving or relieving the challenges above by proposing a new convergence of multi-sink wireless sensor network and passive optical network structure and study the queueing model under a given structure. The other related published work is introduced in the following sections.

\subsection{Backbone Problems}

The applications and the possible applications in future also result in the backbone problems of WSN and it has already be focused recently. Some researchers already studied the method to solve the backbone problems, such as: A novel sleep-scheduling technique called Virtual Backbone Scheduling (VBS) is designed for WSNs which has redundant sensor nodes\cite{backbone1}. In VBS, traffic is only forwarded by backbone sensor nodes, and the rest of the sensor nodes turn off their radios to save energy. Ref.\cite{backbone2} propose BEES, a lightweight bio-inspired backbone construction protocol, that can help mitigate many of the typical challenges in sensor networks by allowing the development of simpler network protocols. Ref.\cite{backbone3} tried to solve the backbone problem for museum monitoring and surveillance. A distributed routing protocol \cite{backbone4} that aims at constructing an energy efficient backbone being convergecast efficient at the same time was proposed and the assistant methods for the backbone were also proposed\cite{backbone5}\cite{backbone6}.

Although all of the above introduced work has tried to solve the backbone problems of WSN and many of them have the good results, they all considered it only in the WSN but not further area. Actually, all the applications are not only inside the WSN but more areas such as access network or core network, because the surveillance and monitoring applications always require the sensed data be transmitted to the human beings who is possible far away the area or parameters which are interested. And the data need to go through all the access and core network to arrive at the monitoring terminal. Consequently, only consider the backbone problem in WSN area is not enough to solve the QoS guarantee requirements and it is also the reason that we tried to consider it in WSN-PON converged structure to solve it.

\section{Passive Optical Networks}

In the following part, the PON and the DBA (Dynamic Bandwidth Allocation) algorithms are introduce because PON is a significant part of the architecture of the converged network and a DBA algorithm based on the modelling work is proposed. Hence, a briefly basic knowledge of them is necessary.

\subsection{PON introduction}

Passive optical network (PON) has been considered as a solution for the subscriber access network for quite some time, even before the Internet spurred bandwidth demand \cite{PONbook1}. It offers low cost and high bandwidth solutions in the last mile service of the Internet access\cite{PONintr3}. Fiber to the Home/ Curb/ Building (FTTx) solutions of PONs can meet the requirements of the services such Internet Protocol (IP) telephony, IP television (IPTV), video on demand and http\cite{PONintr4}. Therefore, deploying a PON between service providers and customer premises can provide a cost efficient and flexible infrastructure that will provide the required bandwidth to customers\cite{PONintr2}.

Generally, PONs are a network in which a shared fiber medium is created using a passive optical splitter/ combinner in the physical plant. Sharing the fiber medium means reduced cost in the physical fiber deployment, and using passive components in the physical plant means reduced recurring costs by not maintaining remote facilities with power. These reduced cost make PONs an attractive choice for access networks, which are inherently cost sensitive\cite{PONintr5}.

All the transmission in a PON are performed between an optical line terminal (OLT) and optical network units (ONUs). The OLT connects the optical access network to the metropolitan-area network or wide-area network (WAN), also known s the backbone or lang-haul network. The ONU is located either at the end-user location (as FTTx).

At a top level, PONs can be classified into several subset: By providing the advantages of low maintenance cost and adaptability to higher bit rates, Ethernet PON (EPON) seems a promising PON technology which has been standardized in IEEE 802.3ah\cite{802.3ah}; Gigabit-capable PON (GPON) is another attractive technology which is standardized in ITU-T G.984 \cite{G.984}. To avoid collision in the PON, time division multiplexing (TDM) or wavelength division multiplexing (WDM)can be used\cite{PONintr3}. Consequently, PONs can also classified as TDM-PON and WDM-PON.

The PON used in the proposed WSN-PON convergence architecture is the TDM-EPON with a physical tree topology, and the mentioned PON in the following part of this thesis is used to represent it. In a PON, the OLT is connected to the ONUs with a feeder fiber that is subsequently split using a 1:N optical splitter/ combiner to enable the ONUs to share the optical fiber. And the transmission direction from OLT to ONU is reffered to as donwstream and operates as a broadcast medium. The transission direction form the ONUs to the OLT is reffered to as upstream, or called uplink.

\begin{itemize}

\item Downstream: In the downstream direction, packets trasmitted by the OLT pass through the 1:N splitter and reach each ONU. The value of N is typically between 4 and 64. This behaviour is similar to a shared-medium network: Packets are broadcast by the OLT and selectively extracted by their destination ONU.

\item Upstream: In the upstream direction, due to the directional properties of a passive optical combiner, data packets from any ONU will reach only the OLT and not other ONUs. In this sense, in the upstream direction, the behaviour of EPON is similar to that of a point-to-point architecture. However, unlike a true point-to-point network, in EPON, all ONUs belong to a single collision domain. Namely, data packets from different ONUs transmitted simultaneously still my collide.

\end{itemize}

As the results of introduced collision problem in upstream above, in the upstream direction, PON needs to employ some arbitration mechanism to avoid data collisions and fairly share the channel capacity among ONUs. That is the DBA algorithm which is introduced in the following section.

\subsection{PON's DBA Algorithms}

The dynamic bandwidth allocation (DBA) algorithms \cite{PONintr2} are defined as the process of providing statistical multiplexing among ONUs and they have been researched a lot. Its major branches of the taxonomy are grant sizing, grant scheduling and queue scheduling.

The DBA algorithms will affect the performance of the convergence network in a large amount of aspects, but might not be the key contribution of our research work, so the algorithms are only introduced generally.

\begin{itemize}

\item \textbf{Grant sizing}

Grant sizing can be divided into four major categories: gated, limited, limited with excess distribution and exhaustive using queue size prediction. Ref.\cite{DBAintr4} and \cite{DBAintr5} gave the analysis of the fixed grant-sizing scheme and Ref.\cite{DBAintr6} and \cite{DBAintr8} analyzed deeply about the delay in the gated ones. The limited grant-sizing technique is studied in Ref.\cite{DBAintr4}\cite{DBAintr9} and the research results illustrate that there is no average packet delay difference between gated and limited grant sizing. Also, some other researchers studied the limited with excess distribution and the result can be found at Ref.\cite{DBAintr10}\cite{DBAintr11}. Queue size prediction is concerned with estimating the traffic that is generated during the period between the REPORT message transmission by the ONU and the beginning of the gated transmission window. Some research used control theory to drive the gap between predicted and actual queued traffic to zero\cite{DBAintr12}, and a higher order liner predictor for predicting traffic during the waiting period at an ONU is proposed in Ref.\cite{DBAintr13}.

\item \textbf{Grant scheduling}

Since grant scheduling works at the inter-ONU level and is coupled with the process of grant sizing, it is performed at the OLT. Typically, to change the scheduling order from round robin, the OLT must wait for all REPORTed queue sizes from the ONUs and then determine the grant order. This requires the use of interleaved polling with stop or the offline DBA framework. There are many published work focused on it: ONU transmissions ordered longest queue first (LQF)\cite{DBAintr9}\cite{DBAintr14} or earliest packet first\cite{DBAintr9} (EPF) have been examined; Simulation results\cite{DBAintr14}\cite{DBAintr15} using Poisson traffic show that both LQF and EPF provide lower average delay at medium loads compared to a round robin scheduler.

\item \textbf{Queue scheduling}

Intra-ONU scheduling is concerned with scheduling the multiple queues of Ethernet frames at an ONU, for transmission within the ONU’s granted transmission window. If the number of queues in an ONU is relatively small, this intra-ONU scheduling can be performed at the OLT. However, as the number of queue increases, scheduling is typically make hierarchical\cite{DBAintr16} with the inter-ONU scheduling at the root of the hierarchy in the OLT and one level of branches. The ideal scheduler should allow statistical multiplexing, but guarantee a minimal portion of the available bandwidth to each priority queue. The generalized processor sharing\cite{DBAintr17} (GPS) achieves this goal for the fluid traffic model, where packets are infinitesimally small. Unfortunately, in practical systems with finite-size packets, the ideal GPS link sharing is not directly applicable because a packet must monopolize the server while in service. The improved versions of GPS are proposed soon, such as WFQ, SFQ and M-SFQ etc.

\end{itemize}

The DBA algorithm proposed in this thesis belongs to the Grant sizing one and some classic DBA algorithms which are compared with the proposed one in Chapter 5 are introduced as the following:

\begin{itemize}

\item Fixed: Each ONU is allocated the same grant size $G_i^{max}$ for every cycle, namely the maximum grant size for that ONU.

Analysis and simulation results \cite{DBAintr4}\cite{DBAintr5} demonstrate markedly inferior performance to the three dynamic techniques below.

\item Balanced: The OLT calculates each ONU's grant size by using the queue length $R_i$ reported by each ONU as a weight:

$G_i=t^{max}_{cycle}R_i/\sum R_i$.

\item Gated: The grant size for an ONU is simply the queue length reported by that ONU: $G_i=R_i$. The average delay is low, but there is insufficient control to ensure fair resource allocation between ONUs. The delay introduced by this scheme has been analysed \cite{DBAintr6}\cite{DBAintr7}.

\item Limited: The grant size is set to the reported queue size up to a maximum grant size for that ONU: $G_i=\min(R_i,G_i^{max})$. Although there is no difference in average packet delay between gated and limited grant sizing \cite{DBAintr4}, limited grant sizing can assist in providing fair access between ONUs.

\end{itemize}

\section{Models of Queueing Theory in WSN and PON}

There are some great contributions of previous researchers who focused on the Modelling work of WSN and PON respectively. But it is hard to find out the related work of modelling work of converged network of WSN and PON. In the following part, the existed models are introduced. Beforehand, some basic knowledge of queueing theory which is used in the modelling work need to be introduced.

\subsection{Used knowledge of Queueing Theory}

\subsubsection{General Introduction of Queueing System}

A queueing system is a place where customers arrive according to an ''arrival process'' to receive service form a service facility\cite{book1}. The service facility may contain more than one server and it is assumed that a server can serve one customer at one time. If an arriving customer finds the service facility occupied (all the servers in this facility are busy or in vacation mode), it joins the waiting queue. This customer will receive its service later in time, either when he reaches the head of the waiting queue or according to some service disciplines (such as higher priority served first), and then leave the system upon completion of his service.

Also, in the paragraph above the words ''customer'' and ''server'' have the different meanings differ from the various application. For example, in the case of computing network (wired or wireless one), the ''customers'' are more often to be used to present the packets (or messages, or cells) that arrive at a switching node (or relay node, or router, or transmission channels \textit{etc}.) which is presented as the ''servers''.

Basically, a queueing system can be broken down into three major components\cite{book1}:

\begin{itemize}

\item the input process;

\item the system structure;

\item the output proces;

\end{itemize}

In the following parts we will discuss the model in this order. Beforehand, the basic structure of the queueing model and the random variables is given.

\begin{figure}

\centering

\includegraphics[width=\textwidth]{Ch2/Modle.pdf}

\caption{Basic queuing system}

\label{f:Basic queuing system}

\end{figure}

\subsubsection{Input process}

We concern ourselves with the following three aspects of the arrival process:

\begin{itemize}

\item[A.] The size of the arriving population;

\item[B.] Arriving patterns;

\item[C.] Behaviour of the arriving customer;

\end{itemize}

In the following part, these three parts are introduced respectively.

\textbf{A. The size of the arriving population}

Generally, the size of the arriving customer population may be infinite in the sense that the number of potential customers form external sources is very large as compared to those in the system, or it may be finite in the sense that the arrival rate is affected by the size.

The size of arriving population gives a significant impact on the queueing results. An infinite population tends to render the queueing analysis more tractable. On the other hand, the analysis of a queueing system with finite customer population size is more involved because the arrival process is affected by the number of customers already in the system \cite{book1}.

Based on it, we will discuss that whether the customer population is infinite or finite in the environment of WSN-PON convergence network, especially for the QoS guarantee of remote surveillance application. Also, the basic random variables of a queueing system are given in Table \ref{t:basicqueuepara} for understanding the analysis of the queueing model.

In the converged network of WSN and PON, as long as the sensor nodes have the energy, the data will be sent to the ONU-Sink. Therefore, from the view of ONU-Sink or the relay nodes in the WSN, it will receive the applications' data continually until the WSN's energy is consumed out. Because the amount of the services' data is much more larger than the one in the system, and for making the system's analysis simple, we suppose that the population of the arriving data is infinite. When the WSN is dead (without energy), it is meaningless to solve the QoS guarantee problem and consider the arriving population. Therefore, the arriving population of the data in the queueing model is considered as infinite.

\textbf{B. Arriving patterns}

Customers may arrive at a queueing system either in some regular patterns or totally random fashions. However, it is significant to fit a statistical distribution to the arriving pattern in order to render the queueing analysis mathematically feasible.

There are probability distributions that are commonly used to describe the arrival process, as shown in Table \ref{t:distributions}.

%\begin{itemize}

%\item $M$:& Memoryless, imply the Poisson process;

%\item $D$:& Deterministic, fixed inter-arrival times;

%\item $E_k$:& erlang distribution of order k;

%\item $G$:& General probability distribution;

%\item $GI$:& General and independent (inter-arrival time) distribution;

%\end{itemize}

In the case of QoS guarantee for remote surveillance application in the convergence network, there are two types of data need to send: one is the scalar data, the other one is the media data. We will discuss it separately.

The scalar data, which describes the temperature, humidity, light intensity or other physical parameters that human beings are interested in, or the information of the sensor nodes such as current energy, routing information and so on, is supposed to be sent to the ONU-Sink when the interested events happen or with regular internal. So it is a process with various stationary probabilities. From the view of ONU-Sink, as it receives many nodes' data as the sum of many point processes, the input process tends to Poisson process\cite{theorembook2}.

Another one is the media data. It has some differences between the scalar and media data:

\begin{itemize}

\item[i.] One of the characters of the media data is its huge amount of the packages and the highly requirement of the time-delay. For remote surveillance always requires to be monitored by voice or video, the amount of data is much larger than the scalar data. Additionally, for the requirements of QoS of media services, the media data requires low time-delay level during the transmission.

\item[ii.] Transmitting the media data need to consume a large amount of energy and need more bandwidth resource. As it is introduced before the media services always have a large amount of data need to send. So it may consume a lot of energy in the sensor node which generates the media services. Meanwhile, the service will be sent to the ONU-Sink by multi-hops. Therefore it will also consume abundant energy of the nodes on its path to the ONU-Sink. On the other hand, because of the highly time-delay requirement, more bandwidth resource is essential in the ONU-Sink so that it can upload more packages in once and decrease the services' waiting time in the queue.

\item[iii.] Last but not least, the media services' data is batch arrived. For the media services are only generated when the special events are happening, the media data is not always received by the ONU-Sink. But once the event happens, the media data will be generated continually for some time since the events are always likely to last for some time. So if the ONU-Sink received a media service data, it is likely to receive another one in the next receiving period. If we consider the each batch as one package, then it follows the Poisson process as we discussed before in scalar data part. Therefore, the media service data follows the batch arrivals according to a Poisson process.

\end{itemize}

\textbf{C. Behaviour of the arriving customer}

Customers arriving at a queueing system may behave differently when the system is full (due to a finite waiting queue) or when all servers are busy. If an arriving customer leaves and is considered lost without entering the system when the system is full, that queueing system is referred to as a blocking system. The analysis of blocking system is more involved.

In our case, the behaviour of the arriving customer depends on the capacity of the queue in each ONU-Sink and the amount of the services' data. Though the amount of the data of the services from the sensor nodes is huge, the capacity of the buffer of the queue in the ONU-Sink is much larger and ONU-Sink always sends the data to OLT very quickly and effectively. So the behaviour of the arriving customer in our special application will be considered as always can get into the queue and wait, namely the capacity of the queue's buffer is infinite.

\subsubsection{System structure}

basic, single-multi multi single-single, open close jackson ...

Fig.\ref{f:Basic queuing system} shows the basic structure of the queueing system (single queue $\&$ single server). Besides this, the queueing system has many different structures. From the view of queue system itself, it has:

\