Jitter Control and Dynamic Resource Management. for Multimedia Communication Over Broadband. Network. Ahmed Bashandy, Edwin Chong, Arif Ghafoor,

Transcription

1 Jitter Control and Dynamic Resource Management for Multimedia Communication Over Broadband Network Ahmed Bashandy, Edwin Chong, Arif Ghafoor, School of Electrical & Computer Engineering, 1285 Electrical Engineering Building, Purdue University, West Lafayette, IN 47907

2 ii Contents List of Figures Abstract iii iv 1 Introduction Multimedia Network Architecture Jitter Control Over Broadband Networks Characteristics of Jitter Link Initial Delay Regulator (IDR) Input and Output Jitter Characteristics of the Initial Delay Regulator (IDR) Relation Between IDR Queue Size and Output Jitter Multiple Node Jitter-Buer Relation Scaling of IDR Dynamic Buer Allocation Buer Allocation Policy for Hard QoS Requirements Fair Buer Allocation Policy with Soft QoS Requirements Simulation and Evaluation IDR Evaluation Conclusion 29 A Appendix 35 A.1 Notations and Symbols A.2 Derivation of Buer-Jitter Relation A.2.1 Problem Denition A.2.2 Peak Transmission Rates A.2.3 Relation Between Buer and Output Jitter

3 iii List of Figures 1.1 Distributed networking architecture Jitter control based on jitter link concept An example of the arrival and departure patterns under IDR control Representing a channel by an eective jitter link An example of OCPN The structure of the simulated node Output jitter vs. average regulator queue size Droppage vs. Average Regulator Buer Size

4 iv Abstract Due to the isochronous nature of multimedia streams, jitter management represents a major challenge to synchronized and timely presentation of multimedia documents. For controlling jitter, we propose the Initial Delay Regulator (IDR). This regulator is based on a network model which abstracts jitter parameters inside a data network. As a result of employing such a regulator, jitter at the destination node can be reduced and possibly eliminated depending on resource availability. The IDR is simple enough to be implemented using specialized hardware. Since IDR is memory intensive, two dynamic resource allocation schemes are presented for hard and soft QoS requirements. The memory allocation schemes have low time complexity to accomodate the highly dynamic nature of multimedia documents. IDR is further evaluated through simulation. Results show that IDR can reduce jitter even for unbounded stocastic trac.

5 1 Chapter 1 Introduction Complex multimedia documents are composed of several component media such as text, audio, image, and video. Industries as well as the government are undertaking major eorts in developing multimedia-based information technologies for manufacturing, medicine, education, business, and entertainment. These technologies are being targeted for the Internet as well as the large number of emergent Intra-nets. Applications range from distributed tele-marketing, tele-medicine, distance education, to industrial monitoring and maintenance. Transmitting multimedia document over a broadband network requires special support from the underlying network protocols. The objective of the network support is to guarantee the quality of presentation (QoP) required by the client at the destination. Typically, a multimedia document consists of several temporally related multimedia objects [24]. Each multimedia object within a document has its own data type which requires specic network handling. Objects with the same data types may require dierent handling requirements depending on the specic properties of the object. For example, two MPEG1 [21] video streams may require dierent bandwidth depending on the individual resolution and the compression ratio. Due to the isochronous and dynamic nature of multimedia documents, relaying multimedia data from a multimedia server to a multimedia client poses a broad range of networking challenges for ecient resource management, intelligent switching, and traf- c shaping. Based on the application QoP requirements [13, 29], the goal is to transmit multimedia data streams from the server to the client while providing guaranteed quality of service (QoS) under diverse network conditions and resource constraints. Several researchers have tackled this problem from a variety of aspects such as end-to-end strategies [8, 9], individual node resource management strategies [10] and QoS-routing strategies [31]. One of the major issues in supporting the QoP guarantees is to provide temporal synchronization at the destination [7]. Synchronization can be classied into two types: intra-stream and inter-stream [32]. The major challenge to a synchronization scheme is the jitter delay experienced over a data network. In [8], experiments show that jitter can have a major impact on buer overow, buer underow and deadline miss at the client side. To further complicate the problem, multimedia streams require exceptionally high bandwidth which hinders the use of complex jitter control schemes and sophisti-

6 2 cated resource management strategies. Switching through high speed networks, such as ATM [22, 30], is usually done through specialized hardware. Hence, simple, yet eective methods for trac shaping and jitter control while eciently utilizing the resources within the network are required if high quality multimedia services are to be supported. Usually, multimedia data is transmitted over established channels. To control jitter over such channels, we propose adding a regulator, which we call the Initial Delay Regulator (IDR), in some or all the nodes along a multimedia channel. The key feature of IDR is its simplicity which allows hardware implementation in high speed networks. Since IDR is memory intensive, we present two buer allocation policies to manage buers at the intermediate nodes and allow fair buer allocation among contending multimedia stream. To analyze the behavior of the IDR and the buer allocation policies, we present a network model that captures the characteristics of jitter inside a data network and abstracts the details of high-speed networks implementations. The concept of jitter is developed based on such network model. In the course of developing the network model, we introduce three notions of jitter: link jitter, input jitter to a node and output jitter at a node. The link jitter represents the variation in the time period between submitting a packet for transmission across a link between two nodes till it is received at the destination node. The input jitter at a node is the variation in the inter-arrival time of packets at the node. The output jitter is the variation in the inter-transmission time or the inter-delivery time to an application. Based on these jitter concepts and the underlying network model, we analyze the behavior of IDR and determine the relationship between link jitter, input jitter, output jitter and buer space inside network nodes. The key issue in the analysis is to compute an upper bound on the output jitter based on worst case behavior of IDR. Such a bound is computed by constructing the packet arrival pattern in an adverserial approach. The objective is to reduce, and if possible, eliminate the worst case output jitter at the destination by introducing IDR in some or all of the intermediate nodes along a channel i.e., to produce jitter-less channels. Using jitter controlled channels, we proceed with the fast resource allocation policies to solve the problem of fair buer allocation among contending multimedia streams. This paper is organized as follows. In the next Section we describe the architecture of the distributed multimedia system. In Section 2, we describe a model that captures the jitter characteristics of the the Broadband Multimedia Network Layer. In Section 3, we introduce the IDR that eectively reduces jitter across a data network. In Section 4, we describe two buer allocation schemes for fair allocation of buer among contending multimedia streams belonging to dierent multimedia documents. Evaluation of of IDR and one of the dynamic buer allocation scheme is presented in Section 5.1 through simulation. Section 6 concludes the paper. Notations and symbols are given in Appendix A.1. The derivation of the properties of the IDR is given in Appendix A Multimedia Network Architecture In this paper, the design of the dierent components of the networked multimedia system is based upon the layered architecture depicted in Fig Such architecture is based on

7 3 the layered architecture proposed in [8]. Each layer is responsible for providing a certain level of sophistication. Multimedia Application Layer: This layer is primarily responsible for maintaining user-perceived quality and the synchronization requirements specied by the users at the time of authoring the multimedia information and documents [25]. This layer is also responsible for oor-control [17] protocols to support work-group types of applications. Distributed Information and Directory Management: This layer is responsible for identifying and locating multimedia information, which is an essential function for the end-user. The functionalities related to this layer include the location identication of media objects that constitute a multimedia document, name resolution, choice of access methods, and address resolution for distributed objects. Thus this layer provides a uniform access mechanism across the information space. The layer incorporates standard searching and browsing protocols, such as web-related protocols including URL (Uniform Resource Locators), HTML (HyperText Markup Language), and HTTP (HyperText Transfer Protocol). Global directories can be used to store meta-data for searching and browsing. Conguration Management: This layer is responsible for establishing appropriate connections types and conguration. The layer determines the type of connection such as unicast, multi-cast and unidirection multi-cast. The CM layer is undertakes the task of setting up intermediate proxy servers and providing clients with the appropriate information about them. Multimedia Synchronization: This layer is primarily responsible for controlling inter-stream and intra-stream synchronization requirements by intelligently scheduling transmission and ltering of media streams, based on the resources available at the client site and reserved by the network. It is also responsible for determining the quality of service parameters based on the specications of the multimedia document. Resource Management: The primary task of this layer is to establish a path between a source node and a destination node such that the quality of service required is guaranteed. To perform this task, the layer computes the required resources and attempts to nd the appropriate path comprising nodes posses the these resources. The layers then proceeds in allocating the resources. Broadband Multimedia Network: This layer is composed of the hardware and software protocols needed to transmit data across a pre-specied path. Several technologies are currently available such as ATM and BISDN [28]. Such technologies have to be augmented by trac shaping and jitter control mechanisms to facilitate QoS routing and end-to-end synchronization. In this paper, we focus on augmenting the Broadband Multimedia Network layer to support jitter control and trac shaping. We propose adding the IDR before the

8 4 Multimedia Application (workgroup, messaging, interactive) Distributed Information & Directory Management Configuration Management Layer (broadcasting, multicasting, point-to-point) Multimedia Synchronization Resource Management Broadband Multimedia Network Computational Backbone Database Backbone Figure 1.1: Distributed networking architecture service discipline in all or some of the nodes to compensate for the jitter experienced across the path. We also propose two dynamic resource allocation schemes to manage the resources at the jitter control nodes. Such schemes are to be integrated into the Resource Management layer as part of the resource management function.

9 5 Chapter 2 Jitter Control Over Broadband Networks Data networks can be viewed as a set of nodes interconnected by communication links. Links can be divided into three categories: point-to-point connections such as telephone lines or SONET/SDH [4, 11] links, shared media networks such as Ethernet [1] and FDDI [2, 3], and virtual circuits through arbitrary data networks. In the rst category, packets experience jitter delay mainly due to queuing. For the second category of links, variations in delay occur due to the shared nature of the transmission medium and is dependent on the physical layer protocol. For token based networks, such as token ring [6], token bus [5], and FDDI, there is an upper bound on the propagation delay, depending on the position of the nodes and the number of active nodes. For CSMA networks, such as Ethernet, it can be shown that there exists a nite bound on the service time of a packet, although such bound can be arbitrarily large [15]. Such service time is the time from submitting a packet for transmission till it is correctly received at the destination which is equivalent to delay across a link. For the third category, the properties of the virtual circuit depends on the underlying protocol and the physical nature of the network. In this paper, we focus on broadband point-to-point communication links and virtual circuits consisting of point-to-point links, such as ATM. In such networks, the interface of a node to the physical layer consists of a server connected to the physical link. Packets that are to be transmitted are queued into tail of an output queue. The server consumes these packets from head of the queue and transmits them across the physical link. In this kind of networks, jitter occurs mainly due to queuing delays. Furthermore, trac is usually throttled at the ingress of the network resulting in deterministically bounded trac characteristics. Such bounded trac can lead to deterministic bounds on the queuing delay if certain queuing disciplines are employed such as PGPS(WFQ) [27] and WF 2 Q [12]. To capture the properties of such networks, we introduce the concept of jitter link to model the Broadband Network layer. Multimedia trac usually traverses this kind of networks through an established channel. This channel can be viewed as a sequence of nodes connected via jitter links. Each jitter link represents the service discipline employed at the node and the physical communication link to which it is connected. To control jitter, we propose inserting a trac regulation mechanism, called Initial Delay Regulator (IDR), inside some or all the nodes

10 6 along a channel to reshape the trac traversing the nodes. The objective is to control the output jitter at the destination. The proposed system is depicted in Fig Multimedia Server Multimedia Application Jitter Link Source Destination Jitter Link Node Node IDR Service Single Link or IDR Service Discipline Virtual Circuit Discipline Figure 2.1: Jitter control based on jitter link concept. In this Section, we start with introducing the concept of a jitter link. We then proceed to describe the concepts of input and output jitter and the characteristics of the IDR. 2.1 Characteristics of Jitter Link As described above, we view the network as a set of nodes connected via jitter links. A jitter link (u; v) connecting the two nodes u and v is characterized by three basic attributes: maximum propagation delay D uv, minimum propagation delay d uv, and minimum interarrival time between any two successive packets, 4 uv. The maximum propagation delay, D uv, is the maximum time dierence between transmitting a packet by node u till it is received at the input of the node v. Such period does not include any residence time at the node u or v. This parameter captures the delay of point to point connections that employ service disciplines which provide bounded queuing delay such as PGPS(WFQ) [27] and WF 2 Q [12]. It can also represent a statistical bound for networks that can have arbitrary large service time. The attribute d uv is the minimum time dierence between transmitting a packet by node u till it is received at the input of the node v. This attribute represents the physical propagation delay and the transmission time. The third attribute, 4 uv, is the minimum inter-arrival period between any two successive packets. This attribute represents the physical transmission capacity of a link. The value of 4 uv must be positive for the capacity to be nite. Our analysis for computing the jitter at the destination node is based on the link jitter J(u; v). The link jitter on a jitter link (u; v) is dened to be the dierence between the

11 7 maximum possible and the minimum possible propagation delays across the link (u; v), i.e.: We make further assumptions to facilitate the analysis: J(u; v) = D uv? d uv (2.1) We assume that the trac originating from the source is transmitted deterministically as one packet per second. Randomness in the packet arrivals at the destination occurs due to the variation in the propagation delay across the jitter links. There is memory space to hold at least one packet. Such memory space is not part of any queue, rather it is an auxiliary memory space for holding a newly arriving packet. For example, it may represent the buer space in a network interface card. This buer space is called the temporary buer space. A packet is moved from the temporary space to the IDR queue as soon as it is received unless the queue is full. 4 uv < 1, for all jitter links (u; v) This assumption ensures that the capacity of the link greater than the transmission rate of the source node u. Packets are received in the same order they are transmitted. That is, if the k th packet is transmitted before the (k + 1) st packet, then the k th packet is received before the (k + 1) st packet. The value of J(u; v) is rounded up to the nearest integer. The concept of jitter link is the foundation of jitter control by IDR. Next we start with introducing other two notions of jitter, namely the input and output jitter at a node. Based on the three concepts of jitter, we describe the IDR.

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13 9 Chapter 3 Initial Delay Regulator (IDR) Jitter management is exercised on a path, p = hv 1 ; v 2 ; ; v n i, between the source node v 1 and the destination node v n. The objective of our analysis is to establish a relation between the output jitter at the destination node and the link jitter of the links and IDR queue sizes of the nodes along the path. This relation is based on the assumption that the nodes along the path employ the Initial Delay Regulator (IDR) for jitter control. We start by analyzing the case where the path is composed of one jitter link (u; v) connecting the two nodes u and v. Based on the assumption that the source node u is transmitting one packet per second, we dene the notions of input jitter and output jitter. We then describe the IDR, giving the relation between input jitter and output jitter at the node v for the path consisting of the single jitter link (u; v). We extend this relation to an arbitrarily long path p = hv 1 ; v 2 ; ; v n i. Finally, we generalize the relation between the output jitter and the IDR queue size to encompass the case where the source node is transmitting packets at an arbitrary rate. 3.1 Input and Output Jitter We start by dening the notions of the arrival pattern and the departure pattern for a node. Let the time dierence between the arrival of the k th packet and the (k? 1) st packet at the node v be denoted by in (k; v). Let the arrival time of the k th packet at the node v be denoted by a k (v). An arrival pattern at node v is dened by the sequence A = ha 0 (v); in (1; v); in (2; v); i: (3.1) Similarly, let the time dierence between transmitting the k th packet and the (k? 1) st packet by the node v be denoted by out (k; v). Let the transmission time of the k th packet by the node v be denoted by t k (v). A departure pattern from the node v is dened by the sequence D = ht 0 (v); out (1; v); out (2; v); i: (3.2) For the two nodes u and v connected by a jitter link (u; v), the input jitter J in (v) at the node v is dened as the maximum possible dierence between the maximum and

14 10 minimum inter-arrival times over all arrival patterns given that the node u is transmitting one packet per second. Since propagation delay must be within the interval [D uv ; d uv ] and based on the assumption that the node u is transmitting one packet per second, we have in (k; v) 6 J(u; v) + 1, achieving equality if the (k? 1) st packet transmitted at time t = k? 1 experiences minimum delay d uv while the k th packet transmitted at time t = k experiences maximum delay D uv. Since the minimum inter-arrival time between any two successive packets is 4 uv, we have 4 uv 6 in (k; v). Hence, the input jitter at node v is given by: J in (v) = J(u; v) + 1? 4 uv (3.3) For the two nodes u and v connected by a jitter link (u; v), the output jitter of node v is the maximum possible dierence between the maximum and minimum inter-transmission times over all departure patterns given that the node u is transmitting one packet per second. That is, J out (v) = maxfmaxf out (i; v)? out (j; v)gg; (3.4) D i;j where the notation \max" denotes the maximum over all departure patterns. D While the relation between input jitter J in (v) and the link jitter J(u; v) is easy to derive as presented in the above Section, the relation between the output jitter J out (v) and J(u; v) depends on the characteristics of the IDR employed inside the node v. In the next Section, we proceed with the description of IDR. Based on this description, we establish the relation between J out (v) and J(u; v). 3.2 Characteristics of the Initial Delay Regulator (IDR) The IDR consists of a queue and a server. When a packet arrives at the node v it is received in the temporary buer space and moved instantaneously to the IDR queue unless the queue is full. Since the source node transmits one packet per second, the IDR is said to successfully remove the jitter if it can forward one packet per second to the subsequent node in a path or to the multimedia application in the case of the destination node. We call the process of delivery or forwarding of a packet transmitting such a packet. Based on this idea of removing jitter, the IDR works as follows. When a node v receives the 0 th packet in a session, it waits for a certain period of time, called the Initial Delay Period (IDP), before starting to transmit the packets at the same rate at which the source node u is transmitting packets. After the IDP, the node v transmits one packet per second whenever possible. In other words, the IDR server examines the queue every a 0 +IDP+k, k 2 f0; 1; 2; : : : g, where a i is the arrival time of the i th packet. If the queue is not empty, the packet at its head is transmitted. We refer to this transmission as a regular transmission. During the course of a session, if the queue of the IDR at the node v is full, and another packet arrives at time t, the IDR server transmits the packet at the head of the queue at time t + 4 uv and moves the new packet from the temporary buer space to the queue so that the next incoming packet does not get dropped. Such a transmission is called forced transmission. Notice that transmitting the packet as late

15 11 as the time t + 4 uv is case of full IDR queue does not risk packet droppage since the minimum inter-arrival time is 4 uv. If a regular transmission occurs prior to or at the time of forced transmission, then the forced transmission does not occur since now there exists an empty space. An example of the arrival and departure patterns under the IDR control is depicted in Fig Notice that since we assumed that there is a temporary buer space, if the IDR queue is full, the newly arriving packet is not dropped. Arrivals at node v Forced Transmissions (buffer overflow) a 0 (v) IDP=J(u,v) Departures from node v Buffer Underflow Figure 3.1: An example of the arrival and departure patterns under IDR control If a forced transmission occurs at time t and a regular transmission is scheduled at time t + ; < 4 uv, then the regular transmission is rescheduled to t + 4 uv instead. The subsequent regular transmission is scheduled at its regular time t As a result, forced transmission does not always occur in case of buer overow. Buer overow is said to occur if a packet arrives at the temporary buer space and nds the IDR queue full. Forced transmissions is one of the sources of output jitter. Another source of output jitter is buer underow. Buer underow is said to occur if at time t = J(u; v) + k for some non-negative integer k, there are zero packets in the IDR queue. Hence, if at some time there are no packet, but a regular transmission is not due, buer underow does not occur. Buer underow is aected by two factors: the IDP and the IDR queue size. The longer the IDP is, the less likely the occurrence buer underow, and the more buer space is required for the IDR queue. As part of the IDR specications, we specify the IDP at the node v for a link (u; v) to be the link jitter, J(u; v). If the IDP is J(u; v), then IDR can never experience buer underow, provided that it has enough buer space for the IDR queue. The following theorem states this fact. Theorem Consider a jitter link (u; v) with attributes 4 uv and J(u; v) = D uv? d uv. If the node u is transmitting one packet per second and the node v has sucient memory, then the IDR at the node v can eliminate the output jitter, i.e. J out (v) = 0. Proof: As before, denote the arrival time of the i th packet at node v by a i (v). Denote the propagation delay of the i th packet across the link (u; v) by i (u; v). We omit u and v whenever there is no ambiguity. Let the node u transmit the 0 th packet at time t = 0.

16 12 Let IDR server at node v transmit one packet per second starting from time t = a 0 (v) + J(u; v) = 0 + J. Then buer underow occurs if at any time t = 0 + J(u; v) + k; k 2 f0; 1; 2; g there are zero packets in the queue. Assume that buer underow occurs for some positive integer k. Since there is enough memory, there are no forced transmissions. Hence, the number of packets transmitted prior to the time t = 0 + J(u; v) + k is k packets (remember that we start counting packets from 0) as the IDR server transmits one packet per second starting from the time 0 + J(u; v). Since there are no forced transmission and the queue is empty, the number of packets received is k. Then the only way for this buer underow to occur is by having a k > 0 + J(u; v) + k. But a k = k + k > 0 + J(u; v) + k ) k? 0 > D uv? d uv () However, note that d uv 6 i 6 D uv for any packet i. Hence maxf k? 0 g = maxf k g? minf 0 g = D uv? d uv which contradicts the inequality (*). Hence a k J(u; v) + k which means there is no buer underow. Referring to Fig. 2.1, the jitter link is used to model an output server connected to a physical link on which it transmits data packets. In general, at a given time, it may not always be possible to transmit a packet since the server may be busy. In the context of the IDR description, we assume that the IDR server will always be able to perform a regular or forced transmission at the time it chooses. This assumption is justied by the fact that transmitting a packet by the IDR server represents moving the packet from the IDR queue it to the appropriate queue of the output server connected to the physical link. The output queue is service discipline dependent. For example, in a FIFO discipline, the packets from all data streams are funneled through a single queue. For WFQ, each data stream has its own queue and the server consumes packets from each queue at a rate that depends on its weight. We assume that the switch is non-blocking, that is, the switch fabric has enough processing power to move packets between queues at the maximum speed they arrive. Hence, the IDR server at a node can transmit a packet whenever it chooses and before any other packet arrives, even if packets are arriving at the maximum possible rate. It is worth noting that using IDR for jitter regulation increases the initial startup time for a multimedia document play-out. However, since we focus on pre-orchestrated multimedia documents, it is jitter rather than the startup time that is the dominant QoS parameter. Having described IDR, we proceed determine to the relationship between the output jitter and the IDR queue size. 3.3 Relation Between IDR Queue Size and Output Jitter Let b(v) denote the size of the IDR queue at the node v. The output jitter J out (v) depends on the queue size b(v), as indicated by Theorem The relation between J out (v) and

17 13 b(v) can be summarized in the following equation: J out (v; b(v)) = 8 < : J(u; v) + 1? b(v)? 4 uv : 1 6 b(v) < J(u; v) 1? 4 uv : J(u; v) 6 b(v) < 2J(u; v) : b(v) > 2J(u; v) + 1 (3.5) The derivation of the above relation is given in Appendix A.2. However, the intuition behind it is as follows. From Theorem (3.2.1), jitter can be eliminated if the node v has enough buer for the IDR queue. The case where b(v) > 2J(u; v) + 1 captures this situation. For the case where J(u; v) 6 b(v) < 2J(u; v) + 1, jitter occurs due to the fact that buer underow can never happen if idr queue size is greater than or equal to J(u; v). Hence jitter occurs only from buer overow which can cause forced transmission resulting in inter-transmission delay as small as 4 uv. The case where 1 6 b(v) < J(u; v) represents the case where both buer underow and overow can occur. Equation (3.5) presents three cases of queue size. For the case where b(v) < J(u; v), the buer-jitter relation is linear. For the case where b(v) > 2J(u; v) + 1, the jitter is zero and packets are transmitted at the rate of one packet per second. For the case where J(u; v) 6 b(v) < 2J(u; v)+1, at most J(u; v) packets experience inter-transmission delays of value less than 1. The reason is that at any time t > a 0 (v), transmission of packets by node v may lag behind arrival of packets by a period of J(u; v) which is the IDP. Such a delay causes a rate mismatch. Hence there may be some bursts due to this mismatch. If the number of packets experiencing inter-transmission periods less than 1 exceeds J(u; v), then the transmission rate is greater than the arrival rate, which is impossible. Hence, for a long data stream, such as a video sequence, the number of packets experiencing inter-transmission delay less than 1 is much less than the total number of packets, and can therefore be ignored. As the result, the signicant relation between queue size and output jitter is given by: J out (v; b(v)) = J(u; v) + 1? b(v)? 4 uv ; (3.6) which holds when 0 6 b(v) < J(u; v). This relation is the basis of our analysis of the output jitter at the destination node of a channel. 3.4 Multiple Node Jitter-Buer Relation The objective is to control the output jitter at the destination of a the channel by introducing IDRs in the nodes along the channel as mentioned at the beginning of this Section. Such a channel can be represented by the path p = hv 1 ; ; v n i from the multimedia server represented by the source node v 1 to the client at the destination node v n. The idea of our analysis is to represent the path p by a single eective jitter link (v 1 ; v n ) as shown in Fig This reduction allows applying equation (3.6) to a compute the output jitter at the destination node. We start by analyzing a path composed of three nodes and then generalizing the result to more than three nodes. Consider the case of the path consisting of three successive nodes hu; v; wi connected via two the jitter links (u; v) and (v; w). The eective jitter along the path hu; v; wi

18 14 Jitter Link u v w Source (v 1 ) Destination (v n ) Effective Jitter Link Figure 3.2: Representing a channel by an eective jitter link. is the dierence between the maximum possible and the minimum possible propagation delay along the path given that the node u is transmitting one packet per second. The maximum and minimum propagation delay can be constructed by the following departure pattern at node v and arrival pattern at node w. Consider the two packets k and (k + 1) transmitted by the node v towards the node w. Let the k th packet be transmitted by the node v at time t k. Let the k th packet experience the minimum delay across (v; w). Let the maximum possible inter-transmission period max occur between the (k + 1) st packet and the k th packet. Let the minimum possible inter-transmission period min occur between the (k + 1) st packet and the k th packet. Let the (k + 1) st packet experience the maximum propagation delay across (v; w). Hence a k (w) = t k + d vw a k+1 (w) = t k + max + D vw Recall that the two packets k and k + 1 are transmitted by the source node u at some time t + k and t + k + 1. Hence the eective propagation delay from the mode u to the node w for the k th and the (k + 1) st packet is given by eective (k) = t k + d vw? t? k eective (k + 1) = t k + max + D vw? t? k? 1 As mentioned in Section 3.3, the signicant relation between the IDR queue size and output jitter is the case where b(v) < J(u; v) + 1 which is presented in equation (3.6). In this case, the value of max can be obtained from Lemma A.2.6 to get J e (u; w) = J(v; w) + J(u; v)? b(v) + 1? 1 = J(v; w) + J(u; v)? b(v) by For a path p = hv 1 ; ; v n i, the eective jitter across the eective link (v 1 ; v n ) is given J e (v 1 ; v n ) = Xn?1 i=2 J(v i?1 ; v i )? b(v i ) + J(v n?1 ; v n ) (3.7)

19 15 Substituting the value of J e (v 1 ; v k ) into equation (3.6), we get nx J out (v n ) = J(v i?1 ; v i )? b(v i )? 4 vn?1 v n + 1 (3.8) i=2 3.5 Scaling of IDR In Section 3.3, the analysis of IDR is based on the assumption that the average rate of transmission is one packet per second. In general, the transmission rate may be higher or lower than one packet per second. In particular, dierent data streams are, in general, transmitted at dierent rates. Since we focus on point to point connections, jitter occurs mainly due to queuing delay in nodes. In many service disciplines [12,20,27], the queuing delay depends on the bandwidth (i.e., the transmission rate) allocated to the data stream in addition to the properties of the stream itself. Hence, we expect dierent streams to experience dierent maximum and minimum delays along the same link (u; v). Consider a jitter link (u; v) where the source node u is transmitting one packet every i second for the i th stream. Let the packets belonging to the i th stream experience minimum delay of d (i) and maximum delay if D (i), and link jitter J (i) (u; v) = D (i)? d (i). Round up uv uv uv uv J (i) (u; v) such that it is divisible by i. The minimum inter-arrival time 4 (i) may also be uv stream dependent if individual streams have minimum inter-arrival time larger than that of the link [18]. As a result, equation (3.5) can be re-written as follows: J (i) out(v; b (i) (v)) = 8 >< >: J (i) (u; v) + i? b (i) (v) i? 4 (i) uv : 1 6 b (i) (v) < J(i) (u;v) i? 4 (i) uv : J (i) (u;v) i i 6 b (i) (v) < 2 J(i) (u;v) i + 1 (3.9) 0 : b (i) (v) > 2 J(i) (u;v) i + 1

20 16

21 17 Chapter 4 Dynamic Buer Allocation Presentation of pre-orchestrated/stored multimedia information requires synchronous playout of time-dependent multimedia data according to some pre-specied temporal relations. At the time of creation of multimedia information (document, etc.), a user needs a model to specify temporal relations among various data (text, image, video and audio) which must be observed at the time of playback. One such specication model is Object Composition Petri-Net (OCPN) [24], that is a timed Petri-net. A place p i in an OCPN represents the play-out process of multimedia data object O i, that may textual data, image or a video/audio segment of certain duration. Attributes associated with an object include the type of data object, its size, its throughput requirement and the duration of its presentation. On the other hand, a transition in an OCPN represents a synchronization point. In other words, it marks the play-out start time of concurrent data objects which are represented by the places at the outgoing arcs of the transition. At the play-out time of multimedia information, the OCPN's structure is executed by following the Petri-net ring rules [24]. For each data object in an OCPN, the time for its play-out is readily determined based on the play-out durations and precedence relations among objects in OCPN. Play-out start time of data object O i is referred to as the play-out deadline P i. At the time of presentation, the OCPN is executed and data objects associated with places are retrieved and communicated to the end user [32]. video(1,1), 1.2 User 1 audio(1,1), 1.2 video(1,2), 1 video(2,2), 1 video(3,2), 1 video(4,2), 1 User 2 audio(1,2), 1 audio(2,2), 1 audio(3,2), 1 audio(2,2), 1 T1 T2 T3 T4 T5 T6 T7 time (b) Figure 4.1: An example of OCPN

22 18 Consider the example shown in Fig At each transition, new multimedia streams are created while others are terminated. Hence, QoS requirements and resource requirements and availability dynamically change at each transition. The algorithms for allocating resources must be executed before starting the transmission of the multimedia object and has to take into consideration the resources that are to be released in the next transition. Fast resource allocation schemes are needed to support the dynamic nature of multimedia documents. QoS requirements can be divided into two categories, hard requirements and soft requirements. For hard QoS requirements, the problem of resource allocation is a combinatorial one and has high computational complexity in general. In addition, resources are not utilized to the maximum possible extent due to the unused portions resulting from the indivisible resource requirements. For soft QoS requirements, intelligent schemes can be employed to increase resource utilization and reduce blocking probability while gracefully degrading the performance of individual sessions. In this Section, we present a buer allocation scheme for each of the QoS requirements categories. Consider a node v traversed by N multimedia streams. The node v is shared by the each of the paths of the multimedia stream. Let the preceding node for the i th stream be u i while the subsequent node be w i. For each stream i, the link jitter J(u i ; v) for the link (u i ; v), the minimum inter-arrival time 4 ui v, and the maximum output jitter J max(v) (i) to its subsequent node w i are given. The input jitter for the i th stream, J (i) (v) in can be computed by substituting J(u i ; v) and 4 ui v into equation (3.3). We assume that J max(v) (i) 6 J (i) (v). In this Section, we omit the arguments in u i, v, and w i., i.e. we denote the link jitter J(u i ; v) by J (i), the input jitter by J (i) (i) in, the maximum output jitter by J max, and the minimum inter-arrival time 4 (i) by uv 4(i). 4.1 Buer Allocation Policy for Hard QoS Requirements One goal of buer policy is to accommodate the QoS requirements of the maximum number of data streams. Another important goal is to maximize the revenue from buer allocation. Maximizing the number of streams is a special case of maximizing the revenue and can be accomplished by setting the revenue of all streams to the same value. For each data stream i, the maximum acceptable jitter J max (i) and revenue v i is specied. By substituting the maximum jitter J (i) max into equation (3.9), the minimum required buer b (i) for the IDR queue can be computed for each stream assuming that J (i) max is multiple of i, the average inter-arrival period. If NX i=1 b (i) 6 B v, then there is enough buer space to accommodate the minimum requirements of all data streams. The available buer can be distributed evenly among the streams to improve the QoS. On the other hand, if some streams cannot be accommodated, then the choice of rejected streams should be based on some policy. From a service provider's point of view, the policy of maximizing the revenue can be very attractive. Such a policy can be

23 19 captured in the following integer program: Maximize Subject To NX i=1 NX i=1 x i v i x i b (i) 6 B v x i 2 f0; 1g b (i) > 0 (4.1) It can easily be shown that such problem is equivalent to a knapsack problem which is known to be NP-complete [19]. This problem can be solved exactly in pseudo-polynomial time using dynamic programming [23]. This algorithm has a time complexity of O(NB v ). Although it provides the optimum solution, the fact that B v is generally in the order of kilobytes precludes the usage of such algorithm in a highly dynamic networking environment. In this paper, we present a fast suboptimal algorithm. To avoid trivialities, we assume that the buer requirement of each individual stream is less than the buer space available in the node. The algorithm is presented in 4.1. Algorithm 4.1 Hard QoS Resource Allocation 1 Compute the minimum memory requirements b (i) based on J max (i) using equation (3.9) 3 Sort the streams in a non-increasing order of v i b (i) 5 i := 1 to produce the sequence S = h1; ; Ni 7 while B v > b (i) in the order of S 9 B v := B v? b (i) 11 i := i end 14 S X := f1; ; i? 1g 15 if v i < max fv i g i2s i2f1; ;N g 16 S := fj : v j = max i2f1; ;N g fv i gg 17 end The output of algorithm 4.1 is the set S containing the accepted streams. The value of the objective function is obtained by adding the revenue values of the accepted data streams. The running time of this algorithm is O(N lg N) due to the sorting step. It can easily be shown that the worst case value of the objective function obtained by the algorithm in not larger than twice the optimum value. Another policy for buer allocation can be based on priority. One way to assign pri-

24 20 ority to individual multimedia streams is to give higher priority to the streams belonging to multimedia documents that are currently being played-out. Let the priority of the i th data stream be z i, the objective is to accommodate data streams in a descending order of their priority. Such objective can be achieved by sorting the streams in the order of their priority and accepting streams in the order they appear. For newly arriving streams, there are three possible alternatives. First, if their buer requirement is less than the remaining buer space after providing the existing streams with their minimum requirement, then the new streams are accepted. If not, the new streams can contend for the remaining buer space according to one of the above policies. In some cases, it may be benecial to terminate one or more of the existing streams and releasing buer space to accommodate the one or more of the new ones. In general, such policy is not applied unless the new streams have very high revenue or very high priority. 4.2 Fair Buer Allocation Policy with Soft QoS Requirements In the previous Section, data streams are either accepted or rejected. In general, multimedia streams tend to have soft QoS requirements [29]. This implies that QoS requirements can be renegotiated and the bounds on jitter can be relaxed. Even if the tolerance of the QoS requirements is small, it is possible for some node to compensate for the poor level of QoS of another node. A natural requirement is to have the degradation in quality distributed fairly among the existing streams. One way to dene a fair buer allocation policy is to demand that if the QoS needs to be degraded, then the degradation should be evenly spread across all the data streams that are contending for resources. Under such fairness criterion, all the streams traversing a node are expected to have roughly equal ratio between their input and output jitter. In this Section, we develop a scheme for buer allocation based on such fairness policy. To facilitate the analysis, we scale equation (3.9) by dividing both sides by i assuming that the jitter J (i) is divisible by i. As a result, for each multimedia stream we get J (i), J (i) out, J (i) in, J (i) max, and 4 (i) leading to the following relation: J (i) out(v; b (i) ) = 8 < : J (i) + 1? b (i)? 4 (i) : 1 6 b (i) < J (i) 1? 4 (i) : J (i) 6 b (i) < 2J (i) : b (i) > 2J (i) + 1 (4.2) The analysis and the algorithm presented in this Section is based on the above scaled relation. Based on equation (4.2), let i be the ratio between the input and output jitter of the i th stream. That is J (i) out = i J (i) in, 0 6 i 6 1. The problem of nding a fair buer assignment, and hence the output jitter for the each of data streams f1; ; Ng, is

25 21 captured by the following non-linear program (NLP) formulation. Minimize Subject To nx X p;q=1 p<q NX i=1 b (i) 6 B v 0 6 i 6 J(i) ( p? q ) 2 max J (i) in ; i 2 f1; ; Ng (4.3) Such NLP, has two problems. First, the parameter b (i) in an integer. Second, even if we relax the integrality constraint of b (i), the relation between buer and jitter dened by equation (3.9) is piece-wise continuous. Hence, conventional methods for solving nonlinear programs cannot be applied. As an alternative, we present a search method which incorporates a rounding scheme, rather than conventional gradient based methods [14,26] to nd an approximate solution. Focusing on the modied NLP problem (4.3), the minimum possible value of the objective function is zero, since all terms are non-negative. If the optimum value of the objective function is indeed zero, then all the the streams have achieved the best possible performance, which is what we desire in the light of the chosen fairness policy. The constraints of the NLP may preclude a solution in which the objective function becomes zero. However, even in such a case, the objective function drives the NLP towards a solution that makes the 's as close to each other as possible, which is conductive to the above-mentioned fairness criterion. When no solution exists for (4.3) and QoS values are indeed soft, we use the following method to determine fair buer allocation for the various data streams. If the NLP (4.3) is infeasible, then the NLP with the following constraints is also infeasible, because for each object i, the new value of i is less than, or at most equal to min, where min = jitter than in NLP (4.3). J (i) min i2f1; ;N g max J (i) in. In other words, in this case we do allow less output Minimize Subject To nx X p;q=1 p<q NX i=1 b (i) 6 B v ( p? q ) i 6 min ; i 2 f1; ; Ng b (i) > 0 (4.4)

26 22 On the other hand, the NLP with the following constraints always has a feasible solution. Minimize Subject To nx X p;q=1 p<q NX i=1 b (i) 6 B v ( p? q ) i 6 1; i 2 f1; ; Ng b (i) > 0 (4.5) A trivial solution is obtained when all the 's are set to one and we do not reshape any of the data streams. Thus b (i) can be reduced to 0, and since B v > 0 by denition, we have a feasible set. Using (4.4) and (4.5) as end points of our search domain, we are guaranteed a solution. The binary search proceeds as in algorithm (4.2).This algorithm has a running time complexity of O(N lg 1). Changing the value of J (i) out from 1? 4 (i) to zero results in a sudden change in the values of b (i) from J (i) to 2J (i) + 1. This change may result in some slack in the buer. In this case, if there are some multimedia streams with J (i) out = 1? 4 (i) that need extra J (i) + 1 buers to eliminate their jitter, then the slack buer space may be distributed among these streams in an ascending order of their requirement, thereby maximizing the number of multimedia streams achieving jitter-less output stream. If the remaining buer size is not enough to eliminate the output jitter of any data stream, it may be distributed evenly which improves the overall performance. The problem with the above allocation policy is that it brings the jitter values of all streams to almost the same values. In many cases, there are data streams that are more sensitive to jitter than other. To further improve the buer allocation policy, we propose grouping data streams with similar jitter requirements into a single group and assigning a buer space to each group. Within each group, data streams can compete for the buer space.

27 23 Algorithm 4.2 Soft QoS Resource Allocation 1 Let the lower bound and the upper for the search period for the i th stream be l i and u i respectively. Set i = min, l i = min and u i = 1. 2 for each iteration 4 if (u i? l i ) 6 ; < 1; 8i 5 2 f1; ; Ng 7 terminate and the output jitter and allocated buer for each multimedia stream is given by the variables J (i) out and b i. 9 end 10 for i := 1 to N 12 JOUT i := i J (i) in 14 if round(jout i ) = 0 16 buf i := 2J (i) JOUT i := 0 20 elsif round(jout i + 4 (i) )? 4 (i) = 1? 4 (i) 22 buf i := J (i) 24 JOUT i := 1? 4 (i) 25 else 26 buf i := J (i) + 1? round(jout i + 4 (i) ) 28 JOUT i := J (i) + 1? buf i? 4 (i) 29 end 30 end 31 if NX i=1 buf i 6 B v ; 32 b i := buf i 8i 2 f1; ; Ng 34 J (i) out := JOUT i 8i 2 f1; ; Ng 36 u i := i 8i 2 f1; ; Ng 38 i := i?l i 8i 2 f1; ; Ng 2 40 else 42 l i := i 8i 2 f1; ; Ng 44 i := u i? i 8i 2 f1; ; Ng 2 46 end 48 end

28 24

29 25 Chapter 5 Simulation and Evaluation 5.1 IDR Evaluation The relation between input and output jitter for IDR is based upon bounded input trac characteristics resulting from the bounded delay variation along jitter links together with the assumption that the source node is transmitting packets uniformly in time. In many cases, incoming trac is stochastic and unbounded. The eectiveness of IDR can be most evident in case of such trac. Further eectiveness can be shown if the output server is a simple one such as FIFO. In this Section, we show the results of simulating IDR in case of a heavily loaded node that uses FIFO as its service discipline. The structure of the node is shown in gure (5.1). Incoming Traffic FIFO Queue Output Link Regulator Bank Figure 5.1: The structure of the simulated node When a packet arrives it is held in the IDR queue until its regular or forced transmission time. Upon transmission, a packet is placed at the tail of the output FIFO queue. The packet is dropped if the FIFO queue is full.