IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS,
VOL. 15,
NO. 8,
AUGUST 2004
673
Distributed Admission Control for Anycast Flows Weijia Jia, Member, IEEE, Dong Xuan, Member, IEEE, Wanqing Tu, Lidong Lin, and Wei Zhao, Fellow, IEEE Abstract—Anycasting has recently become an important research topic, especially for replicated servers. With anycasting, applications can request the “nearest” server for provision of desired (multimedia) service. In this paper, we study efficient Distributed Admission Control (DAC) for anycast flows. We focus on algorithms that perform destination selection and efficient path establishment. Taking advantage of anycasting, our distributed algorithms differ from each other in their dependence on system status information. Performance data obtained through mathematical analysis and simulations show that, in terms of admission probabilities, DAC systems that are based on local status information have performance levels close to those that utilize global and dynamic status information. This renders our DAC algorithms useful not only for the network layer, but also for the application layer admission control for anycast flows. Index Terms—Admission control, anycast service and flow, destination selection, weight assignment.
æ 1
INTRODUCTION
I
N this paper, we study an efficient Distributed Admission Control (DAC) procedure for anycast flows. An anycast flow is a sequence of packets that can be sent to or received by any one of the members in a group of designated recipients or replicated servers. Therefore, throughout this paper, we assume the flows could be bidirectional. Traditional unicast flow can be taken as a special case of anycast flow in the sense that, for the unicast flow, the recipient group size is one. There are many applications that require communication services in the form of anycast flows, e.g., e-transaction, ebanking, downloading, uploading, etc. Using anycast communication services may considerably simplify these applications. Multiple mirrored (replicated) servers of the service providers can share a single anycast address. Applications may simply send their information flows with the anycast address in order to upload or download information to or from these multiple replicated servers. Unlike the case of datagram communication, floworiented communication must go through an admission control process, in which an application makes a request to the network for establishing a flow between a source and a recipient anycast group. An anycast flow can be admitted (or, as we say, the flow can be established) only if sufficient network resources are available to support the requested flows.
. W. Jia, W. Tu, and L. Lin are with the Department of Computer Engineering and Information Technology, City University of Hong Kong, Kowloon, Hong Kong (SAR), P.R. China. E-mail:
[email protected] and {TU.Wanqing, Lin.lidong}@student.cityu.edu.hk. . D. Xuan is with the Department of Computer and Information Science, The Ohio State University, 395 Dreese Hall, 2015 Neil Avenue, Columbus, OH 43210. E-mail:
[email protected]. . W. Zhao is with Texas A&M University, MS 1112, Room 312 Administration Building, College Station, TX 77843-1112. E-mail:
[email protected]. Manuscript received 29 Mar. 2002; revised 26 Jan. 2003; accepted 6 Nov. 2003. For information on obtaining reprints of this article, please send e-mail to:
[email protected], and reference IEEECS Log Number 116186. 1045-9219/04/$20.00 ß 2004 IEEE
Generally speaking, there are two categories of admission control mechanisms: centralized and distributed admission control. Centralized Admission Control. This approach requires a centralized agency to perform admission control for the entire system. The main advantage of this scheme is its simplicity and easy implementation. But, it has problems including single-point of failure and scalability. For a large network, the centralized agency could become a bottleneck. Thus, while this mechanism may be sufficient for small networks, it does not scale adequately to be an effective solution for large systems. . Distributed Admission Control. Distributed admission control mechanism can overcome the scalability problem raised in the centralized admission control. In this mechanism, the admission decisions are made by individual nodes rather than by a centralized agency. In this way, we may achieve better scalability. The challenge here is to let nodes effectively and efficiently coordinate with each other in order to make correct admission decisions, hence achieving higher admission probabilities. In this paper, we assume that a global state of the network is not always available for a node to make admission control decisions on server and route selections. Therefore, we adopt the mechanism of distributed admission control. A critical step in admitting an anycast flow is to select a destination among the members of an anycast (replicated) server group. A destination should be selected so that the requesting flow can be established while not congesting the network. We propose and analyze several algorithms that use different types and amounts of status information in making the destination selection. The DAC is performed by the admission control (AC) nodes (such an AC-node can be a host in the application layer or an edge/ border router in the network layer), thus, not all the .
Published by the IEEE Computer Society
674
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS,
network nodes need to followup the admission control mechanism. Performance data show that, in terms of admission probabilities and efficiency, DAC systems that are based on local status information have performance levels close to those that utilize global and dynamic status information such as available bandwidth, etc. We note that the latter is much more expensive to realize for application layer networks.
2
RELATED WORK
Because more and more applications demand anycast services, in the latest version of IPv6, anycast has been defined as a standard service [1]. The problems pertaining to anycast can be divided into two classes: management methods at the application layer for using anycast services, and procedures and protocols at network layer for routing and addressing anycast messages. In [2], it was determined that anycast addresses are allocated from the unicast address space. An additional set of reserved anycast addresses within each subnet prefix has been also defined in [1]. Some subnet routers can be assigned the reserved anycast addresses that represent all routers within a subnet prefix. A framework for scalable global IP anycast was proposed in [3]. Early work using anycast for locating the nearby replicated server has been proposed in [4]. The anycasting paradigm at the application layer has been examined in [5], [6], in which Zegura et al. have provided an efficient service that uses an anycast resolver to map an anycast domain name and a selection criteria into an IP address. The implication of an anycasting replicated service was also explored through the server push and probe approach. Anycast has been partially defined as a private network-network interface (PNNI) standardization. Frequently used anycast addresses identify access points to key services that are generally distributed on different switches due to high availability; multiple instances of the same address can also exist in the network. Routing to these addresses is similar to routing to exterior addresses. IBM implementation includes the cost of the last hop in computing paths, defined as the cost of the non-PNNI link on which the internal address is defined. Taking this last link into account allows the IBM implementation to compute the best possible paths to these addresses. However, PNNI does not specify how to select a server or path [10]. Q-OSPF [7] is based on routing tables that reflect the global network state. The focus of Q-OSPF is on the algorithms used to compute QoS routes and on the necessary modifications to OSPF to support this function, e.g., the information needed, its format, how it is distributed, and how it is used by the QoS path selection process [8]. However, hop-to-hop OSPF support is indispensable. In [9], QoS routing for anycast communication is discussed in the context of DiffServ networks in which server selection and resource reservation are attained in an aggregated fashion rather than being driven by individual client demand. We have developed several anycast routing protocols and studied their integration with other routing approaches in [11], [12]. Admission control has been studied extensively for unicast flows [13], [14], [15]. The centralized admission
VOL. 15,
NO. 8,
AUGUST 2004
mechanism is easy to implement. For instance, NetEx [16] adopts a centralized admission mechanism to provide endto-end delay guarantees in a LAN environment. Tenet scheme II [17] uses distributed admission control mechanism to achieve scalability, but it needs a signaling protocol for multiparty communication to realize the required functionality. A related technology to distributed admission control is RSVP (Resource Reservation Protocol) [18] that has been proposed for signaling and resource reservation in the Integrated Services architecture. Recently, RSVP has been extended in order to establish label-switched paths (LSPs) in MPLS for a flow along an LSP completely identified by the label applied at the ingress node of the path; these paths may be treated as tunnels [19], [20]. The specifications of TLVs for support of CR-LSPs using LDP for an end-to-end setup mechanism of a CR-LSP initiated by the ingress LSR are given in [21]. Usage-sensitive charging schemes for broadband communications networks has been studied in [24], which described methods of computing usage on the basis of effective bandwidths that can be approximated by charges based on simple measurements.
3
MODELS
Our motivation for the design of the DAC algorithm is for its usage in both application and network layers. Therefore, we make the basic assumption about the underlying network as the current Internet setting. Thus, for the network, the global state is not always available to make the admission control decision for the server and route selections. Nodes are connected by physical links along which packets can be transmitted. Each link has an attribute called link capacity or bandwidth. Link capacity is consumed by anycast active flows. Remaining Capacity or Available Bandwidth of link l, (bl ), at a time instant t, is defined as the part of link capacity on a link which has not been consumed by any traffic at time t. This part of link capacity is available for the new coming flows. An anycast flow is a sequence of packets that can be sent to or received by any one of the members in a group of designated replicated servers. Let A be an anycast (destination) address. We denote GðAÞ to be the group of designated recipients. That is, an anycast flow with anycast address A can be connected to any member in GðAÞ. We assume that anycast flows have a requirement on sequencing. In other words, once the destination of the first packet in the flow is determined, the destination of all the consequent packets in the same flow is fixed. Hence, the destination of a flow is referred to as the recipient node where all the packets in the flow are sent. It is the function of admission control to admit a flow if its bandwidth requirement can be met. The sequence of nodes through which an anycast flow is transmitted from its source (or server) to a destination (or to a user) forms a path or a route. We assume that only the users initiate the anycast flow requests. Several paths may exist from a requestor to one destination in GðAÞ, but without loss of generality, only the shortest path is employed for setup of the connection. This path may be obtained via existing routing protocols, such as OSPF [22].
JIA ET AL.: DISTRIBUTED ADMISSION CONTROL FOR ANYCAST FLOWS
675
Fig. 1. The distributed admission control procedure.
The length of a shortest path can be defined in terms of the number of hops, or by the max-min bandwidth on the path. For simplifying the discussions in this paper, the length of a route is defined as the number of hops on the route. As we will see later, path length will play a critical role in our distributed admission control procedure.
4
DISTRIBUTED ADMISSION CONTROL
4.1 Overview In this section, we study admission control procedure for the requested anycast flows. We have the following objectives in mind: Scalability: Admission control must be scalable as the number of flows increases and as the size of the network expands. Ideally, the overhead of admission control should be independent of the number of flows in the system and the size of the network. . Effectiveness: A good admission control algorithm should maximize the bandwidth utilization to the extent possible. Thus, an ideal system should have a high probability of admitting a new flow if resources are available. . Compatibility: For practical purposes, the proposed admission control mechanism should be compatible with current industrial practices. We intend to avoid modifying the communication and network infrastructure, such as changing the architecture of routers, revising packet format, etc. While all these objectives are important and critical, they may conflict with each other. For example, in order to improve scalability and compatibility, the admission probability may be compromised. To achieve scalability, we adopt the Distributed Admission Control (DAC) mechanism. The overhead caused by admission control is distributed, hence distributed admission control is less sensitive to the system parameters such as the number of the active flows or size of the networks, compared with centralized admission control mechanism. However, a distributed admission control procedure may not attain good performance in terms of admission probability. As we know, to achieve high admission probabilities, nodes that make admission decisions need .
to closely coordinate with others by sharing the global static and dynamic information. The communication overhead among the geographically distributed nodes prevents this kind of information from being shared. Therefore, generally speaking, the effectiveness in terms of admission probabilities may be compromised when distributed admission control is utilized. To address this problem, in the design of our distributed admission control procedure, we consider random distribution of anycast flows along available paths in the network in order to reduce the possible congestion, thus increasing the chance that an anycast flow is admitted.
4.2 Distributed Admission Control Procedure In the Distribution Admission Control (DAC) mechanism, admission decisions for anycast flow establishment requests are made by some nodes at different locations. For the sake of simplicity, in the remainder of the paper, we call the nodes that make admission decisions as Admission-Control nodes (AC-nodes in short). Once a new anycast flow establishment request arrives, the DAC procedure is invoked at the corresponding AC-node for the purpose of admission control as shown in Fig. 1. The DAC procedure consists of three main steps: destination selection, resource reservation, and retrial control. While this procedure is simple, there are two challenging issues: 1) how to properly make destination selection given the limited local information an AC-node contains, and 2) how to efficiently perform resource reservation and path connection. In the following sections, we will discuss our approaches to these issues. 4.3 Destination Selection Destination selection is a special problem in admission control for anycast flows. In this paper, we define the destination as the requested connection destination in the server group and not the flow direction. The uniqueness of destination(s) in unicast and multicast eliminates this problem in their admission controls. This uniqueness introduces a constraint that a flow is connected on the conditions that both the path and the destination must be available. The semantics of anycast defines that an anycast flow can be sent to or received by any member in the anycast group. Nevertheless, we explore how to take advantage of this feature to improve admission probability.
676
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS,
The communication overhead prohibits the AC-nodes from obtaining complete global system status information. Thus, how to select an appropriate destination in the absence of global system information will be a difficult task. In this paper, we adopt a randomized approach for destination selection. Specifically, for an anycast group, an AC-node keeps a list of weights, each corresponding to a destination in the anycast group. Without loss of generality, let us assume that there are K members in an anycast group GðAÞ. Their weights are denoted as W1 ; W2 ; . . . ; WK , respectively. The weight of a destination represents the probability that the destination is selected. Thus, a member with a higher weight will have a higher probability to be selected than those with lower weight values. The assignment of weights will be discussed in the next two sections. Nevertheless, any assignment is subject to the following constraint: K X
Wi ¼ 1:
ð1Þ
i¼1
In this paper, we will study two categories of weight assignment algorithms: unbiased algorithm and biased algorithm. They differ from each other in their treatment of equal destinations and weight assignment.
4.3.1 Unbiased Weight Assignment Algorithm The basic idea of this algorithm is that all the members in an anycast group will have equal probabilities of being selected as the destination for new incoming flows. To force such an even distribution, the weights associated to individual members must be the same, that is, for i ¼ 1; 2; . . . ; K, Wi ¼ 1=K:
ð2Þ
With this algorithm, the anycast flows will be evenly distributed among members of an anycast group, hence we call this algorithm the Even Distribution algorithm (ED in short). This algorithm is simple; it uses no system status information except for the number of members in the anycast group. In general, members in an anycast group, i.e., potential destinations of the anycast flow, are distributed at different locations. There may likely be significant differences among the destinations in the sense of their topological and traffic characteristics, such as distance and load in the paths. Ideally, these differences should be taken into account in terms of destination selection. In the following section, we will propose another category of algorithms, so-called biased algorithms, which consider the above mentioned differences, and we will try to perform selection with certain “discrimination” among destinations.
4.3.2 Biased Weight Assignment Algorithms In this category of algorithms, the members of an anycast group will be treated with certain discrimination in destination selection. Once realized properly, this approach may effectively distribute traffic over different parts of the network, potentially improving admission probability. To fully take advantage of this idea, we must carefully utilize information available to AC-nodes in weight assignment. We propose to use the following information, which can be collected by AC-nodes (with different costs, of course), in weight assignment.
VOL. 15,
NO. 8,
AUGUST 2004
Route Distance Information: For each source, there is one route provided by current routing protocols (such as OSPF) per member in an anycast group. The length of the route is easy to obtain using such protocols [23], [22]. The differences in route distances reflect the different amounts of resource consumption by an anycast flow. Intuitively, the flow to destinations with shorter distances will consume less bandwidth. Hence, a smart destination selection algorithm should discriminate against destinations with longer distances. . Local Admission History Information: It is the record of success in selecting individual destinations in admission control. Recall that a destination selection is successful only if there are sufficient resources along the path that leads to the destination. Obviously, this kind of information is readily available at the AC-nodes; its collection is not costly. However, while this information does reflect network dynamic status, it is not very accurate. . Route Bandwidth Information: The (minimum available) bandwidth of a route represents the minimum available bandwidth of links along this route. This kind of information reflects network dynamic status. However, it is difficult to achieve for the application layer networks. Even in the network layer, it is still expensive without supporting or extending some current unicast (signaling) protocols, such as OSPF or RSVP. In the following, we will consider two algorithms using the above mentioned information in order to make a proper weight assignment. While both of our weight assignment algorithms use route distance information, the first one uses flow admission history information, and the second one uses route bandwidth information. We design the algorithms in this way so that we can investigate how different status information has different impacts on the network performance in terms of admission probability, overhead, and compatibility. Weight Assignment Based on Route Distance and Local Admission History: Here, we propose a destination selection algorithm based on route distance and local admission history information. First, we will introduce a heuristic weight assignment method that takes into account distance information and then extend it to include information on local admission history. We define a route distance as the hop count. As mentioned earlier, a flow with short route distance will consume less resources. Hence, a smart destination selection algorithm should prefer destinations with short route distances. Based on the above consideration, a rule of thumb is that the weight associated with a destination should be inversely proportional to the distances of routes. That is, for i ¼ 1; 2; . . . ; K, .
Wi ¼ 1=Di ;
ð3Þ
where Di is the value of the distance of route leading to destination i. To satisfy (1), the weights should be properly normalized, i.e., for i ¼ 1; 2; . . . ; K, 1=Di Wi ¼ PK : j¼1 1=Dj
ð4Þ
JIA ET AL.: DISTRIBUTED ADMISSION CONTROL FOR ANYCAST FLOWS
Now, we are ready to incorporate the admission history information for dynamic weight assignment. Recall that the local admission history is a log that records the successfulness of selecting individual destinations in admission control. Formally, at an AC-node, this information is represented as a list: H ¼< h1 ; h2 ; . . . ; hK >;
ð5Þ
where K is the number of members in GðAÞ; hi corresponds to the admission history of destination i. The value of hi is defined as follows: At the time of initialization, hi ¼ 0. Every time destination i is selected, taking exponential average on the local history, the following update is made on hi : hi ¼ 0;
if resource reservation returns SUCCESS;
hi þ ð1 Þ; otherwise; ð6Þ where 0 < < 1. That is, the value of hi records the exponential average number of failures in the recent admission history. Through our experiments, we have chosen ¼ 0:1 to emphasize the importance of the most recent history. For example, hi ¼ 0:99 implies that for the last two times when destination i was selected in admission control process, there was insufficient bandwidth and resource reservation returned FAILURE. With the information in list H, the weights at an ACnode are assigned as follows: At the system initialization, the weights are assigned in accordance to (4). Every time a destination selection is about to be made, weights are updated. The basic idea of updating is to reduce the weights of those destinations whose records in list H are not 0, and to increase weights of those whose records in list H are 0. Thus, we first compute the sum of the reduced weights and then evenly distribute the weights to the destinations whose H values are 0. The amount of weights to be reduced is determined by a new parameter (to be discussed later). In particular, the weights are updated in the following three steps: 1.
Calculating the total amount of adjustable weights: AW ¼
K X
Wi ð1 hi Þ:
ð7Þ
i¼1
2.
This step sums up the adjustable weights to AW . is a parameter that is used to adjust the impact of local admission history on weight assignment. If is 0, the local admission history has the maximum impact on weight assignment. At the other extreme, if is 1, the local admission history will have no impact. In our simulation, to emphasize the impact of , we have chosen ¼ 0:1 and the small value of indeed affects the weight assignment when hi 6¼ 0. Updating weights: Wi hi ; if hi 6¼ 0; ð8Þ Wi0 ¼ Wi þ AW =M; otherwise; where M is the total number of destinations whose records in list H are 0. This step is to reduce the
677
3.
weights of those destinations whose records in list H are not 0, and increase the weights of the destinations whose records in list H are 0. Normalizing weights: W0 Wi ¼ PK i 0 ; j¼1 Wj
ð9Þ
where Wi0 is given in (8). This step guarantees that the weight assignment satisfies (1). Given that this weight assignment algorithm uses both the route distance and local admission history, we refer to this algorithm as Weighted Distribution with route Distance and local admission History information (WD/D+H in short). We expect that its admission probability will be higher than that of the Even Distribution (ED) algorithm. However, the local admission history is coarse and may not accurately reflect the network dynamic status. In the following sections, we propose an algorithm using onroute bandwidth information, which is better than the local history. Weighted Assignment Based on Route Distance and Available Bandwidth: Here, we assume that the bandwidth usage of links on routes to all destinations are available. Let r be the route from the source to destination i. Route Bandwidth Bi is defined as: Bi ¼ minðbl Þ; l2r
ð10Þ
where bl is the available bandwidth of link l. Hence, Bi represents the minimum available bandwidth of links along route r to destination i. Intuitively, the destination whose route has more route bandwidth should have a higher possibility of being selected. Thus, the available bandwidth based weight assignment for a destination i is proportional to Bi , i.e., Wi / Bi =Di . To normalize the weight, we can extend (4) as follows: Bi =Di Wi ¼ PK ; i¼1 Bi =Di
ð11Þ
where Bi and Di are route bandwidth and route distance of the route from the source to destination i. Since this weight assignment algorithm uses the route distance and route bandwidth information, we refer to it as Weighted Distribution based on route Distance and available Bandwidth algorithm (WD/D+B in short). We expect that WD/D+B will achieve better performance than the previous one. In order to assign the weights, we have to know the route bandwidth information. For this, we have to extend some current signaling protocols. For example, if RSVP is adopted, we have to extend it to let the RESV message carry this kind of information back to AC-nodes. Thus, WD/D+B is much more expensive than other approaches and it is difficult to achieve the compatibility with the application layer admission control. On the other hand, collecting the network global information is costly for a large scale network. In brief, we have introduced three destination selection algorithms. They differ from each other on using system information: the ED algorithm uses no system status information except the number of members in the anycast group, WD/D+H algorithm uses the routes distances and
678
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS,
VOL. 15,
NO. 8,
AUGUST 2004
Fig. 2. Parallel DAC algorithm.
local flow admission history information while WD/D+B uses the routes distances and bandwidth information.
4.4
Efficient Resource Reservation and Route Control Recall that, in our distributed admission procedure, once a destination is determined, the next step is to reserve resources along the route from the source (represented by the AC-node) to the selected destination for the requesting flow. The connection must be setup for the flow transmission. As we mentioned before, the destination selected cannot guarantee that the route selected can be successfully setup. In this section, we explain the route set up as well as the algorithm that maximize the possibility that a route can be successfully set up. 4.4.1 Resource Reservation We assumed that the routes from the source to the destination in an anycast group are predefined (such as the shortest path). Hence, the resource reservation involves only two simple tasks: Task 1: Confirm whether or not there is sufficient bandwidth available on all the links of the route. If there is not, FAILURE will be returned by the DAC procedure. Otherwise, . Task 2: reserve bandwidth on each of the links along the route, and report SUCCESS by the DAC procedure. The resource reservation can be made by RSVP-TE protocol [18], [19]. That is, to check the availability of link bandwidth along the route, we can use some polling and reserving messages, such as RESV and PATH messages available with RSVP. .
4.4.2 Retrial Control Once resource reservation returns SUCCESS, the route with enough bandwidth is setup, the newly requesting flow will be admitted, and it will be offered to the route which leads to the selected destination. However, if the route cannot be established, a decision must be made if an alternative destination should be attempted. However, there is a trade off. On one hand, to improve the admission probability, more destinations should be attempted. On the other hand, the more destinations tried, the more is the overhead (e.g., the
communication overhead due to resource reservation messages) introduced. We use a simple counter-based retrial control scheme. Initially, a counter c is set to zero. Each time a destination is tried, c is increased by one. The retrial control returns true if c is less than a predefined parameter R. R is the total number of retrials allowed. Through our experiments (not shown in the paper due to lack of space), in the retrial scheme, we found that the retrial number R ¼ 2 provides the highest improvement over the admission probability.
4.4.3 Parallel Path Control Although retrial will enhance the admission probability for the flows, the retrial process also substantially increases the admission delay. In this section, the retrial control is improved to be a parallel version (thus, called parallel DAC) while multiple destinations are selected for connection at the same time. The parallel DAC intends to reduce admission time while trying to attain a high admission probability as compared with the retrial scheme. Parallel (multipath) routing has been studied in the unicast routing extensively [30], [31]. It has advantages of tolerating a single path failure and enhancing route reliability. However, this scheme cannot cope with the destination failure problem, e.g., once a destination is not available, the final step of multipath routing may still fail no matter how many paths have been established. The shortcoming of multipath routing for unicast can be easily eliminated in the scenario of anycast. Since an anycast flow may be connected to any one in a group of members, the possibility of simultaneous unavailability of multiple destinations is very low. Therefore, our multipath routing focuses on different destinations, and for each destination, only one path is invoked. We consider those destinations with weight Wi > 0 as the available destinations for selection. We redesign the algorithm in Fig. 1 as a parallel version shown in Fig. 2, in which k destinations with the highest weights are selected for the parallel multipath connections by an AC-node. However, there are several problems associated with the parallel DAC algorithm: 1.
Parameter k must be determined. In general, a parallel multipath connection will ensure a higher possibility of admitting a flow. However, more connections also introduce substantial overhead to
JIA ET AL.: DISTRIBUTED ADMISSION CONTROL FOR ANYCAST FLOWS
2.
3.
5
the network. Similar to the retrial number R ¼ 2, we propose k ¼ 2 in the parallel DAC algorithm. Reserved but unused routes should be handled. In the parallel DAC algorithm, multipaths may connect successfully, but only one path is used. In general, there are two ways to handle the unused route: release it immediately or reserve it for the use of another request as long as a requested flow can be accommodated. But, deciding the reservation time is difficult as it is unpredictable for future arrival requests. Thus, the unused route should be released immediately if it is not used by any newly arrived request at the AC-node. Overhead of setting up the parallel routes as compared with the retrial control must be considered. There is clearly a trade off between the retrial and parallel control schemes. The parallel DAC indeed reduces the admission delay time, but the network cost may increase. This issue is detailed in Section 6 through performance comparisons.
ANALYSIS
In this section, we employ an analytical method for computing admission probability. To simplify the discussion, we will focus on two systems. One uses the Even Distribution (ED) as its destination selection algorithm with retrial once. We denote such a system as system (ED, 1). Another system uses the Shortest Path (SP) algorithm to do the destination selection where the selected destination is the one with the shortest distance. We denote such a system as system SP. The method presented here can be extended to other systems (under certain approximation assumptions). We will not discuss the extensions here due to space limitations.
5.1 Problem Definition We consider a network that consists of N nodes and L links. Let link l ðl ¼ 1; 2; . . . ; LÞ have capacity Cl . Let GðAÞ be an anycast group with K members. We denote S to be the set of sources of anycast flows. We assume that all the anycast flows have the same bandwidth requirement, say b. Let ðs; GðAÞÞ denote the stream of flow requests from source s to anycast group GðAÞ. The arrivals of flow requests from stream ðs; GðAÞÞ form a Poisson process, with mean rate s . Let Rðs; GðAÞÞ be the set of routes for stream ðs; GðAÞÞ.1 If a flow request in stream ðs; GðAÞÞ is offered to route r 2 Rðs; GðAÞÞ, it may be blocked and rejected if there is insufficient bandwidth available on any link in route r. If the flow is admitted, the bandwidth on each link is simultaneously held for the duration of the flow. The holding period (i.e., the lifetime) of a flow in stream ðs; GðAÞÞ is assumed to be exponentially distributed with mean 1=s . Hence, the demanded traffic intensity from s to GðAÞ is s ¼ s =s . Let the portion of anycast traffic from source s in set S offered to route r 2 Rðs; GðAÞÞ be s;r . In system (ED, 1), the 1. Assume that the shortest routes from the sources of anycast flows to the anycast group are given. Hence, in the DAC procedure, if the destination is selected, the route for a newly arriving anycast flow is determined accordingly.
679
anycast traffic from s is uniformly distributed among the routes in Rðs; GðAÞÞ, i.e., s;r is given by s =K, for any r in Rðs; GðAÞÞ:2 In system SP, all the flows are offered to the route with the shortest path in Rðs; GðAÞÞ. Thus, s;r is equal to s if r is the shortest path in Rðs; GðAÞÞ; otherwise, s;r is 0. We use Ls;r to denote the rejection probability of anycast flows from source s to GðAÞ given that they are offered to route r 2 Rðs; GðAÞÞ. Then, the admission probability (P), of the network can be expressed as follows: P P s r2Rðs;GðAÞÞ s;r ð1 Ls;r Þ P P : ð12Þ P¼ s r2Rðs;GðAÞÞ s;r With (12), once Rðs; GðAÞÞ and s;r for each s in S are given, P can be obtained if Ls;r can be computed. Hence, the problem of deriving P is reduced to that of deriving the rejection probabilities of individual routes, i.e., Ls;r .
5.2 Analyzing Route Rejection Probabilities In this section, we focus on analyzing the rejection probabilities of individual routes, i.e., Ls;r . The analysis is based on the well-known and often used link independence assumption [25]. With this assumption, we reduce the problem of analyzing route rejection probability to that of analyzing the link rejection probability. We then apply the fixed point method in conjunction with the Uniform Asymptotic Approximation (UAA) approach to compute link rejection probabilities [26], [27]. The derivation of the fixed point equations is also based on the link independence assumption. Let Bl denote the rejection probability of link l. This is the probability of a flow request being rejected because of insufficient bandwidth on link l. Under the link independence assumption [25], the route rejection probability Ls;r is now given by Y ð13Þ Ls;r ¼ 1 ð1 Bl Þ; l2r
where r 2 Rðs; GðAÞÞ. With (13), as long as link rejection probabilities are computed, the route rejection probability can be obtained. In the following, we proceed to discuss how to compute the link rejection probability. Recall that link l has capacity Cl and an anycast flow requires bandwidth b. Let vl be the reduced load obtained after “thinning” (reducing) of flow requests offered to link l. It is clear that the link rejection probability of link l, i.e., Bl , depends on b, vl , and Cl . Here, we use function ð:Þ to denote such a dependence. That is, Bl ¼ ðb; vl ; Cl Þ. Note that, since b and Cl are constant, it can be simplified as follows: Bl ¼ ðvl Þ:
ð14Þ
On the other hand, the reduced load of link l, i.e., vl , depends on the rejection probabilities of other links. We use function ’ð:Þ to represent such a dependence. As we know, each route which uses link l contributes a load to link l, with 2. Note that the anycast traffic is not necessarily uniformly distributed among its routes in the systems using our other proposed destination selection algorithms. For instance, in the system using < W D=D þ H > and < W D=D þ B > , the anycast traffic is distributed among its routes based on the information of distance (D), historical information (H), or available bandwidth (B). Definitely, such a distribution is not uniform.
680
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS,
a rate which is thinned by all other links in the route. Again, according to the link independence assumption [25], such thinnings could be assumed independent both from link to link and over all routes containing link l. Hence, we have: vl ¼ ’ðB1 ; B2 ; . . . ; BL Þ Y X X s;r ð1 Bm Þ: ¼ s
r2Rðs;GðAÞÞ
ð15Þ
m2rflg
Synthesizing (14) and (15), we have the following fixed point equations. For l ¼ 1; 2; . . . ; L, Bl ¼ ðvl Þ; ð16Þ vl ¼ ’ðB1 ; B2 ; . . . ; BL Þ: ’ð:Þ is given by (15). Once ð:Þ in (16) is determined, Bl can be solved by using the fixed point method which works as ð0Þ follows: This method starts with initial values vl . It then ðiþ1Þ iterates with the following formulas: For i ¼ 0; 1; . . . , Bl ¼ ðiÞ ðiþ1Þ ðiþ1Þ ðiþ1Þ ðiþ1Þ ðvl Þ and vl ¼ ’ðB1 ; B2 ; . . . ; BL Þ, where l ¼ 1; 2, . . . ; L. The iteration continues until a convergence criterion is satisfied. The remaining issue is how to determine function ð:Þ. In this study, we apply the uniform asymptotic approximation (UAA) approach [26], [27] to do so. The UAA approach relies on the following assumptions: For link l, Cl 1 and vl ¼ OðCl Þ, where Cl is the capacity of link l, which is an integer [26], [27].3 This means the asymptotic regime for the UAA is large link capacity and large offered traffic load on the link. As a matter of fact, according to [26], [27], extensive numerical investigations found that, for moderately large link capacity and offered traffic load not large relative to the link capacity, the error in the blocking probabilities computed by the UAA is below 1.5 percent. However, when the link capacity is small, say less than 50, then such levels of accuracy cannot be expected. The networks we study have high link capacity. In part of our performance evaluations, the link capacity of the network is 100 Mbps, 20 percent of which is reserved for anycast traffic. The minimum bandwidth of a request is 64K. Then, the link capacity in unit is about 320, which is much larger than 50 and, hence, high accuracy can be achieved. Having discussed the assumptions and the features of the UAA, we now define: Fl ðzÞ vl ðz 1Þ Cl log z; ð17Þ Vl ðzÞ vl z: Following the derivation in [26], [27], we have eFl ðz Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; M 2Vl ðz Þ
ð18Þ
where zl ¼ Cvll and 3. Here, the values of the link capacity are translated to the number of units. The unit can be the minimum bandwidth of a request.
NO. 8,
AUGUST 2004
M¼ 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F ðz Þ sgnð1zl Þ > 1 epl ffiffiffiffil pffiffiffiffiffiffiffiffi1ffi > p ffiffiffiffiffiffiffiffiffiffiffiffiffi ; > 2 Erfc½sgnð1 zl Þ Fl ðzl Þþ 2 > Vl ðzl Þð1z Þ 2Fl ðzl Þ > > < zl 6¼ 1; > vl 1 1 > pffiffiffiffiffiffiffiffiffiffiffi > 2 f1 þ 2Vl ð1Þ ½1 þ 3Vl ð1Þg; > > > : otherwise: ð19Þ The complementary error function and the sign function are given by Z 1 2 2 ErfcðyÞ ¼ pffiffiffi ex dx: ð20Þ y In the next section, we will evaluate our proposed algorithms in terms of the admission probability (P) of the anycast flows. We take the following steps to compute P: 1.
2. 3.
6
We first use the fixed point method to solve (16) to get the link rejection probability. Function ð:Þ and ’ð:Þ in (16) follow (15) and (18), respectively. We apply (13) to get the route rejection probabilities. We use (12) to compute P.
EXPERIMENTAL EVALUATION
In this section, we evaluate performance of systems that use our distributed admission control procedures with different destination selection algorithms, and compare between the retrial and parallel control schemes.
6.1
Experimental Model
6.1.1 Network Two types of networks are considered in our experiments. The first one is the MCI ISP backbone (called MCI) network as shown in Fig. 3. There are 19 nodes that are interconnected by links. The second type of networks are randomly generated from 1,000 random nodes with a general-purpose random topology generator BRITE [32]. BRITE is specially designed to generate Internet-link network topologies that exhibits the power-law for the distribution of node degrees [33]. That is, the number of nodes with a given degree d is proportional to d , where is a constant. Such a network can be generated in two steps. First, n nodes are randomly placed in a rectangular area (this process is called node placement). Then, a bidirectional link is added according to RouterW axman model [35]; that is, nodes are incrementally added to the network. For each pair of nodes, a distance is chosen in ð0; LÞ from a uniform random distribution and L is the maximum distance between the two nodes. Edges are introduced between pairs of nodes u, v with a probability that depends on the distance between them. The edge probability is given by P ðfu; vgÞ ¼ exp
Bl ¼ ðvl Þ
VOL. 15,
dðu; vÞ ; L
where dðu; vÞ is the distance from node u to v, and are parameters in the range ð0; 1. Larger values of result in graphs with higher edge densities, while small values of increase the density of short edges relative to longer ones. In our experiment, we set ¼ 0:15 and ¼ 0:2. The network is set with random connections. Thus, the average (maximum)
JIA ET AL.: DISTRIBUTED ADMISSION CONTROL FOR ANYCAST FLOWS
681
Fig. 3. The experimental network.
number of hops between any source and destination is 6 and 10, respectively, and the average degree of connection for a node is 4. Every node is a router and has one host attached. All networks in our simulations are assumed as the guaranteed-rate scheduling networks, i.e., once a connection is set up, certain amount of bandwidth is reserved for the flow and the end-to-end delay requirement of the flow transmission can be guaranteed. Thus, we do not model the queuing behavior for the routers within the networks. In the MCI network, link bandwidth capacity is set to 100Mbps. In the random topology networks, the link bandwidth capacity is assigned a value chosen in the range of [50Mbps, 500Mbps] on a uniform random distribution. In both cases, 20 percent of link bandwidth is reserved for anycast flows. Our simulator is Mesquite CSIM C [34], a process-oriented, general purpose simulation toolkit. All the simulations ran in 10 SUN Ultra-SPARC workstations.
6.1.2 Traffic Model We assume that requests for anycast flow establishment form a Poisson process with rate , while flow lifetimes are exponentially distributed with average of 180 seconds. Two flows with bandwidth requirements of 64kbps, 1.2Mbps, and 5Mbps, representing audio, standard MPEG-1, and MPEG-2 DVD streams, are used in the experiments. Sources of anycast flows are chosen randomly among those hosts attaching to the nodes with odd number identities. In the MCI network, there is an anycast group with five members attaching to nodes 0, 4, 8, 12, and 16, respectively. For random (1,000 nodes) networks, 10 random topologies were generated for each of the experiments and we collect the average data. The flow requestors are chosen randomly among those nodes with odd identities and sent to five anycast groups. We randomly selected 25 nodes among all the nodes in the network with even number identities. Then, the 25 nodes are (randomly) partitioned into five groups, each containing five members. 6.1.3 Evaluated Systems Recall that a pair ðS; AÞ is used to represent the systems which run our proposed DAC with different destination selection, retrial, and parallel control algorithms. In particular, S represents the destination selection algorithm. That is, S 2 fSP ; ED; W D=D þ H; W D=D þ Bg:
ð21Þ
A 2 f1; 2; P g indicates the maximum number of retrials that are allowed when A ¼ 1; 2. Parallel connections are invoked when A ¼ P . For example, (ED, 2) represents a system in which Even Distribution (ED) algorithm is used, and the maximum number of retrial routes is 2. For parallel control, we set k ¼ 2 for the experiments in various systems; as we discussed before large values of k (say k 3) may not improve the system performance very much.
6.1.4 Performance Metrics First, we are interested in Admission Probability (P). It is defined as the probability that an anycast flow is admitted in a given system. The higher the P value is, the better the performance we have. The second metric we study is the average number of the hops visited for setting-up a path. Recall that both R and k are directly proportional to the overhead in terms of resource reservation messages (network cost) and admission delay. The smaller the number of hops involved, the more efficient the system is. 6.1.5 Evaluation Methods Both mathematical analysis and computer simulations are used in obtaining performance data for the MCI network. Specifically, we found that the admission probability of systems we considered can be analyzed by queuing theory and fixed point method as described in Section 5. 6.2
Comparison of Mathematical Analysis and Simulation Data As we mentioned in Section 5, several approximation assumptions in our mathematical analysis are made in order to simplify the computation. Here, we compare performance data obtained by (approximately) mathematical analysis and computer simulations for MCI network in order to validate the properness of assumptions made. Tables 1 and 2 show the admission probabilities of system (ED, 1) and SP, respectively, as a function of flow arrival rates by both analysis and simulations. The network and traffic model are the same as described in previous sections. From Tables 1 and 2, we observe that the values of admission probability obtained by both analysis and simulation are almost identical. The next section illustrates the experiments obtained from various networks with realistic input flows.
682
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS,
VOL. 15,
NO. 8,
AUGUST 2004
TABLE 1 Comparison of Mathematical Analysis and Simulation Methods in (ED, 1)
TABLE 2 Comparison of Mathematical Analysis and Simulation Methods in SP
6.3 Performance Observations In this section, we report performance results and make observations. We only present a limited number of cases here. However, we find that the conclusions we draw here are generally true for many other cases we have evaluated.
6.3.2 Comparison of Retrial and Parallel Control Sensitivity of P to parallel DAC systems: Fig. 5 shows the sensitivity of admission probabilities of systems ED, WD/D + H, and WD/D + B with 2 parallel path setup in two types of networks. As expected, system WD/D + B outperforms other two systems in both networks. In the MCI network, the performance of ED performs very closely to that of WD/D + H and even slightly better when the arrival rate is low (for instance, less than 10). This demonstrates that when the network is lightly loaded in a small network, a simple approach may be effective. While in the 1,000 nodes random network, the situation is different. As shown in Figs. 5c and 5d, when the arrival rate is higher, Fig. 5c shows that system (WD/D + B) outperforms system (WD/D + H). This is because the system with larger bandwidth capacity may admit more requests; Fig. 5d shows the system (WD/D + H) performs closely to that of (WD/D + B). This is because, when the arrival flow rate becomes higher, then less bandwidths are available for 5Mbps flows, which is much larger than 64Kbps as shown in Fig. 5c. Since system (WD/D + H) only
6.3.1 Sensitivity of Admission Probability Comparisons on P of the systems in different networks: Fig. 4 shows the admission probabilities of systems SP, (ED, 2), (WD/D + H, 2), and (WD/D + B, 2) in different networks (MCI and 1,000 nodes random generated topology). It can be seen that all the three systems, (ED, 2), (WD/D + H, 2), and (WD/D + B, 2), outperform SP. (WD/D + B, 2) is the best among the three due to its access to the route bandwidth information. We also noticed that, in terms of P, (WD/D + H, 2) outperforms (ED, 2). In the 1,000-node networks, when arrival rate of flows increases, we have the similar observation. Of course, system WD/D + B always has the best performance, however, it requires the support of underlying system to provide the available bandwidth information and this may not be available for application layer networks.
Fig. 4. Admission probability of different systems under retrial = 2. The first two figures are with the MCI network under rate = 64Kbps and 1.2Mbps, accordingly. The other two figures are with 1,000 nodes random topology including five groups under rate = 64Kbps and 5Mbps, respectively.
JIA ET AL.: DISTRIBUTED ADMISSION CONTROL FOR ANYCAST FLOWS
683
Fig. 5. Admission Probability of Different Systems under k = 2. The first two figures are with the MCI network under Rate = 64Kbps and 1.2Mbps, accordingly. The other two figures are with 1,000 nodes random topology including five groups under Rate = 64Kbps and 5Mbps, accordingly.
requires its local history information to make the decision on destination selection, high arrival rate of flow requests may bring the most recent local history information to facilitate the AC-node to make destination selections in reflecting the current network congestion. To compare the performance in terms of P and overhead of a system using retrial and parallel control schemes, we discuss, in the following, the performance comparisons of the two systems. Fig. 6 shows the sensitivity of admission probabilities of system WD/D + H under retrial and parallel control path setup under various networks and traffic load. The figure shows that the P for parallel control is fairly close to the retrial control. The overhead comparisons made in Fig. 7 demonstrate the average time for the admission delay and network cost (denoted as TIME and COST, respectively) in terms of number of hops. In the retrial control, the connection is set sequentially, thus, the average hop counts for both admission delay time and network cost are the same. However, in the parallel control, the network cost may double that of delay time in terms of number of hops. As expected, (WD/D + H, P) performs closely to (WD/D + H, 1) in terms of admission delay (TIME) and outperforms (WD/D + H, 2) when the arrival request rate is high. On the other hand, the COST of system (WD/D + H, P) initially is high. With higher arrival rate, the overhead is close to that of (WD/D + H, 2). The statistics shown here give the insight that systems (WD/D + H, 1) and (WD/D + H, P) can be adaptively applied in response to the arrival rate of the requesting flows. Fig. 8 shows the performance of P using system (WD/ D + B) under MCI network and 1,000 node random networks. We found that P is insensitive to either retrial or parallel controls. This is because system (WD/D + B) needs the information of the available bandwidth for the
destination and path selected. Neither trials nor parallel control can help to increase P very much. For the overhead observation, it is similar to that of using system (WD/D + H), however, the underlying routing protocol cost (i.e., RSVP) has not been taken into account.
7
CONCLUSIONS
We have studied the Distributed Admission Control (DAC) procedure for anycast flows with three algorithms: ED, WD/D + H, and WD/D + B. These algorithms differ from each other in their dependence on system status information. The destination selection based on WD/D + H algorithm is novel in the sense that it only uses the local information to make the destination selection. Thus, it provides an efficient (heuristic) service for anycast flow requests as comparable to the method that uses global dynamic network information. This is very useful if the destination selection decision is made only through the application layer network. We address the issues related to resource reservation to ensure the compatibility with existing protocols, and we have improved the DAC into a parallel version that can greatly enhance the admission probability and reduce the admission delay. Our proposed DAC procedure is effective in the sense that it can achieve much higher admission probability. In our extensive performance evaluation, we show that the system with (WD/D + H) and (WD/D + B) can outperform system (SP) in the range of 20 percent to 60 percent in terms of admission probability, which is a baseline system for anycast flows. Our DAC is scalable. The nature of distributed control mechanism can help achieve high scalability by distributing the admission overhead to multiple nodes (i.e., AC-nodes). Also, with our route selection algorithm, our AC-nodes only need to keep the group-based information rather than per
684
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS,
VOL. 15,
NO. 8,
AUGUST 2004
Fig. 6. Admission probability in system (WD/D+H,*). The first two figures are with the MCI network under Rate = 64Kbps and 1.2Mbps, respectively. The other two figures are with 1,000 nodes random topology including five groups under Rate = 64Kbps and 5Mbps, respectively.
anycast flow information, which further reduces the overhead of the AC-node. Finally, our DAC procedure is compatible with current industrial practice. Only some edge nodes (i.e., AC-nodes) conduct the DAC procedure and no change is introduced at the network core.
The QoS requirement we considered is implicitly limited to bandwidth as discussed in the previous sections. In the networks with priority-driven schedulers, we can follow the approach presented in [29] to transform the delay requirement into an upper bound on bandwidth that need to be
Fig. 7. Cost of system (WD/D+H,*). The first two figures are with the MCI network under Rate = 64Kbps and 1.2Mbps, respectively. The other two figures are with 1,000 nodes random topology including five groups under Rate = 64Kbps and 5Mbps, respectively.
JIA ET AL.: DISTRIBUTED ADMISSION CONTROL FOR ANYCAST FLOWS
685
Fig. 8. Admission probability in system (WD/D+B,*). The first two figures are with the MCI network under Rate = 64Kbps and 1.2Mbps, respectively. The other two figures are with 1,000 nodes random topology including five groups under Rate = 64Kbps and 5Mbps, respectively.
reserved, hence we convert the delay related QoS to bandwidth-based QoS.
[6]
[7]
ACKNOWLEDGMENTS This work is partially supported by the Research Grant Council (RGC) Hong Kong, SAR China under grant contracts CityU 1055/00E (9040687) and CityU 1039/02E (9040596), and CityU strategic grant under contracts 7001355 and 7001446. Dong Xuan’s work was supported in part by the US National Sceince Foundation under contract ACI-0329155. Wei Zhao’s work was supported in part by the US National Science Foundation under contract EIA-0081761, by the Defensive Advanced Research Projects Agency under contract F30602-99-1, and by the Texas Higher Education Coordinating Board under its Advanced Technology Program. The authors are grateful to the reviewers for their valuable comments that helped to improve the revised version. Part of this paper appeared in The 21st IEEE International Conference on Distributed Computing Systems, 2001.
[15]
REFERENCES
[16]
[1] [2] [3] [4] [5]
S. Deering and R. Hinden, “Internet Protocol Version 6 (IPv6) Specification,” RFC 2460, Dec. 1998. R. Hinde and S. Deering, “IP Version 6 Addressing Architecture,” RFC 1884, Dec. 1995. D. Katabi and J. Wroclawski, “A Framework for Scalable Global IP-Anycast (GIA),” Proc. SIGCOMM 2000, pp. 3-15, 2000. J.D. Guyton and M.F. Schwartz, “Locating Nearby Copies of Replicated Internet Servers,” Proc. SIGCOMM, pp. 288-298, Oct. 1995. S. Bhattacharjee, M.H. Ammar, E.W. Zegura, V. Shah, and Z. Fei, “Application-Layer Anycasting,” Proc. IEEE Infocom, pp. 13881396, 1997.
[8]
[9]
[10] [11]
[12] [13]
[14]
[17]
[18]
E.W. Zegura, M.H. Ammar, Z. Fei, and S. Bhattacharjee, “Application-Layer Anycasting,” IEEE/ACM Trans. Networking, vol. 8, no. 4, pp. 455-466, Aug. 2000. R. Guerin, A. Orda, and D. Williams, “QoS Routing Mechanisms and OSPF Extensions,” Proc. IEEE GLOBECOM, vol. 3, pp. 19031908, 1997. G. Apostolopoulos, D. Williams, S. Kamat, R. Guerin, A. Orda, and T. Przygienda, “QoS Routing Mechanisms and OSPF Extensions,” RFC 2676, IETF, 1999. F. Hao, E.W. Zegura, and M.H. Ammar, “QoS Routing for Anycast Communications: Motivation and an Architecture for DiffServ Networks,” IEEE Comm. Magazine, pp. 48-56, June 2002. “Private Network-Network Interface Specification v.1.0,”Technical Report af-pnni-0055.000, ATM Forum, Mar. 1996. D. Xuan, W. Jia, W. Zhao, and H. Zhu, “A Routing Protocol for Anycast Messages,” IEEE Trans. Parallel and Distributed Systems, vol. 11, no. 6, pp. 571-587, June 2000. W. Jia, D. Xuan, and W. Zhao, “Integrated Routing Algorithms for Anycast Messages,” IEEE Comm., vol. 38, no. 1, pp. 48-53, Jan. 2000. A. Dailianas and A. Bovopoulis, “Real-Time Admission Control Algorithms with Delay and Loss Guarantees in ATM Networks,” Proc. Infocom, pp. 1065-1072, 1994. V. Firoiu, J. Kurose, and D. Towsley, “Efficient Admission Control for EDF Schedulers,” Proc. Infocom, pp. 310-317, 1997. J. Liebeherr, D.E. Wrege, and D. Ferrari, “Exact Admission Control in Networks with Bounded Delay Services,” IEEE/ACM Trans. Networking, 1996. A. Sahoo, B. Devalla, Y. Guan, R. Bettati, and W. Zhao, “Adaptive Connection Management for Mission Critical Applications over ATM Networks,” Int’l J. Parallel and Distributed Systems and Networks, special issue on network architectures for end-to-end quality-of-service support, vol. 3, no. 2, pp. 51-63 2000. R. Bettati, D. Ferrari, A. Gupta, W. Heffner, W. Howe, M. Moran, Q. Nguyen, and R. Yavatkar, “Connection Establishment for Multiparty Real-Time Communication,” Proc. Fifth Int’l Workshop Network and Operating System Support for Digital Audio and Video, pp. 240-250, Apr. 1995. L. Zhang, S. Deering, D. Estrin, S. Shenker, and D. Zappala, “RSVP: A New Resource Reservation Protocol,” IEEE Networks Magazine, vol. 31, no. 9, pp. 8-18, Sept. 1993.
686
IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS,
[19] D. Awduche, L. Berger, D. Gan, T. Li, V. Srinivasan, and G. Swallow, “RSVP-TE: Extensions to RSVP for LSP Tunnels,” RFC 3209, Dec. 2001. [20] E. Rosen, A. Viswanathan, and R. Callon, “Multiprotocol Label Switching Architecture,” RFC 3031, Jan. 2001. [21] B. Jamoussi, L. Andersson, R. Callon, R. Dantu, L. Wu, P. Doolan, T. Worster, N. Feldman, A. Fredette, M. Girish, E. Gray, J. Heinanen, T. Kilty, and A. Malis, “Constraint-Based LSP Setup Using LDP,” RFC 3212, Jan. 2002. [22] J. Moy, “OSPF Version 2,” RFC 1583, Mar. 1994. [23] C. Hedrick, “Routing Information Protocol,” RFC 1058, June 1988. [24] C. Courcoubetis and F. Kelly, “Measurement-Based Usage Charges in Communications Networks,” Operations Research, vol. 48, no. 4, pp. 535-548, Apr. 2000. [25] F.P. Kelly, “Blocking Probabilities in Large Circuit Switched Networks,” Advanced in Applied Probability, vol. 18, pp. 473-505, 1986. [26] D. Mitra, J. Morrison, and K. Ramakrishnan, “ATM Network Design and Optimization: A Multirate Loss Network Framework,” Proc. Infocom, 1996. [27] D. Mitra and J.A. Morrison, “Erlang Capacity and Uniform Approximations for Shared Unbuffered Resources,” IEEE/ACM Trans. Networking, vol. 2, no. 6, pp. 558-570, 1994. [28] C. Li, R. Bettati, and W. Zhao, “Static Priority Scheduling for ATM Networks” Proc. IEEE Real-Time Systems Symp., 1997. [29] S. Wang, D. Xuan, R. Bettati, and W. Zhao, “Providing Absolute Differentiated Services for Real-Time Applications in Static Priority Scheduling Networks,” Proc. Infocom, pp. 669-678, 2001. [30] I. Cidon, R. Rom, and Y. Shavitt, “Multi-Path Routing Combined with Resource Reservation,” Proc. IEEE INFOCOM, vol. 1, nos. 712, pp. 92-100, Apr. 1997. [31] I. Cidon, R. Rom, and Y. Shavitt, “Analysis of Multi-Path Routing,” IEEE/ACM Trans. Networking, vol. 7, no. 6, pp. 885896, Dec. 1999. [32] A. Medina, A. Lakhina, I. Matta, and J. Byers, “BRITE: Boston University Representative Internet Topology Generator,” http:// cs-pub.bu.edu/brite/index.html, Mar. 2001. [33] M. Faloutsos, P. Faloutsos, and C. Faloutsos, “On Power-Law Relationships of the Internet Topology,” Proc. SIGCOMM, pp. 251262, 1999. [34] Mesquite Software Inc., http://www.mesquite.com/products/ csim19.htm, 2003. [35] B.M. Waxman, “Performance Evaluation of Multipoint Routing Algorithms,” Proc. IEEE INFOCOM, pp. 980-986, Mar. 1993. Weijia Jia received the BSc, MSc, and PhD degrees, all in computer science, in 1982, 1984, and 1993 from Center South University, China and Polytechnic Faculty of Mons, Belgium. He joined the German National Research Center for Information Science (GMD) in St. Augustin in 1993 as a research fellow. In 1995, he joined the Department of Computer Science, City University of Hong Kong (CityU) and, currently, he is an (adjunct) associate professor of the Department of Computer Science and the Department of Computer Engg&IT at CityU. His research interests include computer network, distributed systems, multicast and anycast QoS routing protocols for Internet and wireless communications. In these fields, he has published more than 150 papers and books/chapters in the international journals and conference proceedings. He has been the Principal-Investigator of 18 research projects supported by RGC Research Grants, Hong Kong and Strategic Research Grants, CityU. He has served as PC cochairs and PC members for various IEEE international conferences. He is a member of the IEEE.
VOL. 15,
NO. 8,
AUGUST 2004
Dong Xuan received the BS and MS degrees in electronic engineering from Shanghai Jiao Tong University (SJTU), China, in 1990 and 1993, and the PhD degree in computer engineering from Texas A&M University in 2001. Currently, he is an assistant professor in the Department of Computer and Information Science, The Ohio State University. He was on the faculty of Electronic Engineering at SJTU from 1993 to 1997. In 1997, he worked as a visiting research scholar in the Department of Computer Science, City University of Hong Kong. From 1998 to 2001, he was a research assistant/associate in the Real-Time Systems Group of the Department of Computer Science, Texas A&M University. His research interests include real-time computing and communications, network security, and distributed systems. He is a member of the IEEE. Wanqing Tu received the BEE degree in electronics and information systems from Nanchang University, Nanchang, China, in 1999, and the MSc degree in computing networks from Zhongshan University, Guangzhou, China, in 2002, respectively. She is currently a research student in the Department of Computer Engineering and Information Technology, City University of Hong Kong. Her research interests include peer-to-peer computing, anycast, and mobile computing.
Lidong Lin received the BSc and MSc degrees in applied mathematics from Jinan University, Guangzhou, China, in 1999 and 2002, respectively. He is currently a research student in the Department of Computer Engineering and Information Technology, City University of Hong Kong. His main research interests include network applications and services and mobile computing.
Wei Zhao completed his undergraduate program in physics at Shaanxi Normal University, Xian, China, in 1977. He received the MSc degree and PhD degree in computer and information science from the University of Massachusetts, Amherst, Massachusetts, in 1983 and 1986, respectively. He is currently an associate vice president for research at Texas A&M University. In 1990, he joined Texas A&M University where he has been a full professor in the Department of Computer Science since 1996. Between 1997 and 2001, he served as a department head. His current research interests includes secured real-time computing and communication, distributed operating systems, databases, and fault tolerant systems. His research group has been recognized by various awards and prizes and he is an inventor for two US patents and has published more than 180 papers in journals, conferences, and book chapters. Dr. Zhao was an editor of the IEEE Transactions on Computers between 1992 and 1996. He currently is on the editorial board of the IEEE Transactions on Parallel and Distributed Systems. He has been program and general chairs of many IEEE international conferences. He is an IEEE Fellow.
. For more information on this or any other computing topic, please visit our Digital Library at www.computer.org/publications/dlib.
