On the Economics of Interconnection among Hybrid QoS Networks in the Next Generation Internet
Junseok Hwang and Martin B. H. Weiss
[email protected]
[email protected]
Telecommunications Program University of Pittsburgh Pittsburgh PA 15260
April 14th, 2000
Abstract
How do different QoS (Quality of Service) mechanisms affect the resource and quality allocations over the interconnection of the future Internet? What will be the consequences on the economics of interconnection and its settlements? These are important questions that arise with the evolution of the Internet as a network of QoS networks that support a variety of performance requirements. The convergence of various telecommunications networks relies critically on the interconnections of various networks and related QoS management and assurance. Furthermore, the heterogeneity of the proposed QoS support mechanisms intensifies the importance and integrity of these research questions related to the network interconnection.
In this paper, we will address the economic problems of network resource management over hybrid-QoS networks. This study proposes that interconnecting QoS networks will manage both QoS pricing and QoS bandwidth allocation for optimal interconnection, and different QoS networks will have different optimal QoS allocation policies due to different marginal costs (marginal bandwidth opportunity cost) associated with each QoS
mechanism and policy. These costs will be estimated from the results of network simulation using statistics of traffic flow measured from a current Internet backbone. This study also asserts that the QoS allocations of individual networks will be highly affected by the economizing behavior of interconnecting networks under uncertainty without commitment.
We will use the statistical results of network simulation to present the numerical example of those cost functions with respect to the contracted QoS for DiffServ QoS networks. We also develop the network economic models that provide the means for bandwidth management. The model captures characteristic of opportunity costs and demands, and suggests the strategies on QoS pricing and allocation. By using these economic models, we numerically simulated the behavior of a DiffServ’s bandwidth broker to optimize its payoff strategies for practical assumptions. We expect that the implication of this paper will be useful to both ISP network planners and regulators concerning with the interconnection issues of the next generation Internet.
Keywords: IP QoS, ATM, IntServ, DiffServ, RSVP, QoS Economics.
1. Introduction The convergence of various telecommunications network relies heavily on the interconnection of various networks and related QoS (Quality of Service) management and assurance. Currently, the Internet is evolving into a next generation network which supports various QoS applications in addition to best effort services. The interconnection of the next generation Internet is hindered by various new problems that are different from the issues of conventional telephone interconnection and the best-effort Internet interconnection. Those challenging issues of the next generation Internet interconnection include hybrid QoS interconnection, service coordination, traffic engineering and QoS allocation among the heterogeneous QoS-support networks.
There is an important rationale for examining the hybrid QoS networks in this study. Most importantly, the technical motivation of hybrid QoS management in the next generation Internet is scalability. Some hybrid QoS-network approaches to enhance the scalability of the QoS-support networks have been proposed by the IETF working group ISSLL (Integrated Services over Specific Link Layer). Those hybrid network approaches include IntServ over DiffServ, IntServ over ATM and other variants. Yet these approaches have not addressed the potential problems of QoS allocations when a QoS connection traverses various hybrid-QoS networks. In addition, different QoS networks have different cost characteristics for different levels of QoS service. This study will investigate how such cost of quality of different QoS networks will characterize the optimal interconnection strategies of individual network service providers and motivate them to interconnect with each other.
The economics of various hybrid interconnections depends on not only the bandwidth costs but also other service related factors such as pricing, service classification, and demand characteristics. We will deal with those relevant network economic factors in the scope of QoS interconnection.
In this paper, we introduce the technical framework for the hybrid-QoS interconnection. We will propose some mechanisms for the realization of QoS interconnection for currently proposed IP QoS support architectures such as DiffServ and IntServ. Then we develop network economic models to characterize the different service and performance properties of various QoS architectures in IP networks. Finally we introduced an optimization problem to address the optimal interconnection behavior of the ISP network providers. This problem is motivated by the fact that the ISPs may act non-cooperatively for QoS Interconnection when there is not enough information. To assess the values of the parameters of those economic models for various QoS networks, we use simulation to dimension networks with various size and capacity. We used the cost data of best effort network interconnection to estimate the cost functions of different networks. Using the cost functions of various QoS networks and selected QoS pricing strategies, we captured service strategies of QoS networks.
2. Technical Background 2.1 Quality of Service (QoS) The importance of supporting quality of service in packet switching network, especially in the Internet, has recently intensified. The use of the Internet has changed in character and grown in both scale and scope. Increased applications' traffic raises several issues including resource contention, efficient use of bandwidth, enhanced level of service quality, or at least protection from service degradation. All of these issues are closely related to the concept of ``quality of service'' (QoS) that is the network service performance measure thanks to the differential treatment of packets in the network ranging from queueing, and service discipline to service contract to protocols. Levels of QoS concerns with the following different QoS measures; bandwidth, delay and delay jitter, throughput and loss rates.
The QoS measure of bandwidth concerns with the data rate assured from the network service as a level of QoS, especially in times of network congestion. The QoS bandwidth can be specified in the forms of minimum data rates, average data rates, effective data rates and peak data rates. Frame relay and ATM provide popular contracted QoS bandwidth arrangement. Such QoS bandwidth support capabilities are developed in the IP networks with the help of the RSVP signaling protocol and effective aggregate bandwidth managed by BB (Bandwidth Broker) in the IntServ and DiffServ QoS Models, respectively.
The QoS measures of delay and delay jitter refer to the bounded end-to-end latency and its variation of packets of QoS services as selected levels of QoS latency. Bounded endto-end delay and jitter are, especially, important QoS measures to real time applications such as internet telephony and internet video conferencing. For example, a maximum of 150 msec of end-to-end delay is recommended by the ITU for toll quality voice application. The increased jitter requires that an additional delay budget be allocated to the dejitter buffer at the receiver. If a packet is delayed beyond the required end-to-end delay bound, the packet becomes no longer relevant in terms of QoS for a real time application receiver. Such an excessive delay will have the receiver drop the packets,
which results in the waste of bandwidth and in turn degrades the overall QoS of applications. Bandwidth reservation, packet differentiation, queueing strategy, and rate control scheduling are approaches to bound this QoS latency used in various forms in the different QoS mechanisms.
Throughput as a QoS measure is the amount of data that can be transferred in a given amount of time. Unlike the bounded delay, the throughput is a useful QoS measure for a non-real time application. The QoS level sets amount of data that will be transferred in a given time. ATM and Frame Relay provide such QoS throughput assurance in the form of so called CIR (Committed Information Rates). It is a useful QoS measure for aggregate data traffic which is sensitive to packet loss.
Loss rate as a QoS measure determines the maximum number of packets expected to be lost within a specified transfer time due to network congestion and other network failures. The network nodes such as routers and switches drop packets from the output queues to relieve the network congestion and excessively delayed packets might be dropped at the receiver. The QoS level required for loss rate varies among different applications. General voice and audio applications are known to tolerate loss rates up to around 10-2 to 10-3 because they still can retrieve intelligible voice and audio at such a QoS level.
2.2 QoS-Support Mechanisms in the Internet The Internet uses packet switching technologies. ATM and IP are currently the two main packet switching techniques equipped with QoS-support for multiservice networks for the use of the Internet. Both ATM and IP assign the network resources based on statistical multiplexing, and support the required performance of various applications statistically. ATM is designed to support the various quality requirements of applications which are supposed to be carried over various AAL (ATM Adaptation Layer) class cells in ATM. These classes are assigned to various services such as CBR, VBR, UBR, and ABR. On the other hand, the Internet was initially designed as a so-called best-effort network which does not support any type of end-to-end QoS-support.
Various techniques to support QoS using IP protocols have recently been proposed. This is a fundamental departure from the traditional best-effort network nature of current Internet, however there are still many issues to be addressed in order to implement the appropriate QoS mechanisms. Those proposed QoS-mechanisms include IntServ (Integrated Services) and DiffServ (Differentiated Services). IntServ seeks to support connection oriented QoS service on top of IP networks for specific connections and flows based on media-specific (application specific) behavior. DiffServ is the approach of keeping the philosophy of connectionless Internet and of supporting QoS at the aggregate level of applications based on the PHB (per hop behavior) of the packet. Finally, the simplest way of achieving the required QoS is providing enough network resources (overengineering) to avoid the high network loads that result in delays and delay jitter. This approach is widely used through the LAN and private network environment to provide IP QoS service over packet networks. In summary, the protocol stack of QoSsupport protocols for WAN applications is illustrated in Figure 1. In this paper, we will consider DiffServ and IntServ of IP networks.
Figure 1: The Protocol Stack of QoS-Support for WAN Application Applications Higher Layer Protocols TCP/UDP DF, AF, EF
BS, CLS, GS
DiffServ/IP
IntServ/IP
CBR/VBR ABR/UBR
AAL
ATM MPLS / MPOA / Layer2 SONET, DS3, Other Physical Layer
2.3 QoS Interconnection and Hybrid-QoS Model Architecture QoS-Interconnection involves the interconnection among heterogeneous QoS-support providers with different QoS-support technologies and service definitions. There are many possible combinations of QoS mechanisms for interconnection. QoSinterconnection is important because it assures end-to-end QoS-support for end-users by
satisfying the end-user application requirements and enables efficient interconnection by optimizing the settlements metrics of interconnections among different network providers.
Even though there are several interconnection architectures of QoS-support networks possible, only some are practical and scalable for the backbone Internet. For example, RSVP of IntServ has a scalability problem and the priority approach implemented in DiffServ model does not provide as strong an assurance of end-to-end QoS as RSVP and ATM does. In addition, ATM tends to be more used for core backbone services than for end-to-end services in practice. Due to these constraints, only some alternatives of the hybrid QoS-interconnection are worth evaluating for practical QoS interconnection models. Those alternatives include Overen-DiffServ, Overen-IP/ATM, IntServ-DiffServ, DiffServ-IP/ATM, and IntServ-IP/ATM. All of these assume that DiffServ and IP/ATM are scalable enough for backbone network transport protocols which can aggregate similar traffic into its engineered aggregate service classes or virtual circuits.
It is unlikely that all the backbone network providers will employ same QoS-mechanisms to support the required QoS to the connections of aggregate applications of their networks. All of these hybrid approaches require the mappings of per-flow service quality to aggregate behavior quality and vice versa. For example, RSVP-DiffServ or IP/ATM-DiffServ mappings require new traffic engineering approaches to provide the reserved flow bandwidth into different admissions to differentiated aggregate services. In this paper, we will focus on the QoS interconnection of IntServ-DiffServ hybrid QoS networks.
3. A Technical Framework of QoS Interconnection This section briefly summarizes the technical requirements of QoS mechanism for the hybrid interconnection. Considering currently proposed QoS support approaches, we will discuss the implementation details of connecting different QoS networks. Even though there are many IP QoS support mechanisms proposed, no interconnection mechanisms have been developed yet to support fair levels of QoS guarantee and provisioning options
among different IP QoS mechanisms for hybrid QoS interconnection. The framework here will investigate the resource management mechanisms of QoS interconnection at the protocol layers three and four of IntServ-DiffServ hybrid QoS networks.
The framework will be presented for our study by classifying hybrid QoS interconnection mechanisms along several tasks. Followings are the main functional tasks for the resource allocations of hybrid QoS interconnection. ? ? QoS Guarantee and Admission Control ? ? Service Code Mapping, Aggregation, and Provisioning ? ? Bandwidth Management The QoS guarantee is the task of supporting a comparable QoS guarantee among different QoS support approaches. For example, there should be mechanisms for supporting aggregate level QoS guarantee (DiffServ or Overengineering) comparable to be provisioned to the flow level QoS guarantee (IntServ). One of the tasks to assure the provisional level of QoS is done through admission control. However, admission control for the aggregate level QoS networks has not been developed as a standard yet in the Internet community. The admission control proposed here is for the use of aggregate QoS networks such as Overengineering and DiffServ networks through the operation of bandwidth manager (BM) or also called bandwidth broker (BB).
The block diagrams presented below show admission procedures for the aggregate QoS domain of flow based network services and the according Per-Hop-Level QoS management functions, respectively. Figure 2 provides the procedural flow for the admission control is used for RSVP flows within DiffServ domain using Bandwidth Broker. The assigned PHB and its associated provisioning Bandwidth will be assigned as a certain admission priority token value for the use of DiffServ. The bandwidth broker will manage the accumulated admission priority token values for each IP bit pipe (IP tunnel in the example) and regulate it for each pair of ingress and egress nodes.
Figure 2: Bandwidth Management Admission Control
No
Admission of RSVP
Yes
Class and Priority Assignment to Tunnels
Rejected Service
Priority Regulator at each Hop of the Tunnel
BBs Manage End-to-end Tunnel
Cumulate Value of Priority on each Tunnel of the DiffServ
Differtiated Service Performanece at the provisioned level
The summary of the proposing QoS guarantee procedure can be expressed as follows: ? ? Any QoS flow requesting network services from the aggregate QoS network will be assigned appropriate PHB classes. ? ? Each PHB class has finite priority values associated with each IP bit pipe provisioned between each ingress and egress node. ? ? The combination pair of priority value and capacity provision will be assigned for the finite number of priority token values for admission control. Therefore, there will be limited numbers of priority token values used for each IP bit pipe. ? ? PHB class assignment is done at the ingress for the flow signaling (PATH), and the priority token value will be assigned and evaluated on the returning ingress
(RESV) which will initiated the admission control of Bandwidth Broker of the networks. ? ? The routing of the IP bit pipe should be designed to support the use of the priority token values to regulate the router transmission of the IP bit pipe. For example, packet enabling and non-preemptive priority scheduling should be controlled by bandwidth broker for the guaranteed QoS level. ? ? The cumulative class priority values and priority token values will be stored in each router for each IP bit pipes. The accumulated values at all nodes of each IP bit pipe will be used for the admission control to reject or admit RSVP setup signaling.
Figure 3 demonstrates that this class admission should be working closely with QoS routing at the aspects of bandwidth managers. The QoS routing should be designed to closely cooperate with this bandwidth management function.
Figure 3: DiffServ Per-Hop-Behavior Operation Bandwidth Broker BW Management
Priority Accumulator
QoS Routing Management
Class Based Queueing
Differentiated Services Service Classfier
IP Tunnel
EF CSF AF DF
The second tasks in the hybrid IP QoS networks is related to how we characterize the traffic through code assignment, class aggregation, and provisioning of the bandwidth. Approximation methods of aggregate bandwidth for different scale of traffic and different QoS requirement will be needed. In conjunction with the first task, admission control,
the algorithm of estimating aggregate bandwidth in the operation of Bandwidth Broker will be required.
The third task is how to optimize the resource allocations within the domain of aggregate QoS networks, and allocate or outsource QoS to the neighboring network when the capacity is constrained. Within the flow based QoS network only, there is no concern about bandwidth management since it is done for each flow connection at the edge of the network in a distributed fashion. However, for the aggregate QoS networks such as DiffServ networks, the function of bandwidth management should be utilized in a way to perform the global optimization of resource allocation for different QoS network services in aggregate basis.
4. Network Economic Models of QoS Networks Assuming the technical framework of QoS interconnection network, several different models for different QoS network will be presented. The economic models encompass the models for cost, demand, pricing, and interconnection. The theoretical network economic models are developed to characterize different economic variables and properties of different QoS networks. One of the motivations of the development of network economic model is to formulate the optimization framework for the bandwidth management for QoS networks. Interconnecting different QoS networks raises many new network economic questions. For example, what is the difference in service selection and pricing when the network is offered in a single QoS networks and when it is offered in a hybrid QoS interconnecting network. Will there be mutual interests in terms of service selection, quality allocation and pricing among different QoS network providers? What will be the quantitative methods of resource allocation of QoS network services when the cost sharing is necessary? To study these network economic questions, we formulated economic models for DiffServ QoS networks.
4.1 Cost Models of QoS-support Networks First, we assess the cost functions that will be used in our analysis. The bandwidth manager will assess the cost of the network service based on the estimation of network
usage and the market value of the bandwidth. The estimation of the network usage can be assessed through the information access for the accumulated values of token priority values or measurement, and the market value of the bandwidth might be assessed through the dynamic price information of bandwidth commodity market. Therefore, the cost function we present is not the real capital cost functions but the opportunity cost model which represent the shadow price of different network services.
The economic costs of bandwidth and QoS will be assessed for the different types of QoS networks through the dimensioning using the methods of simulation. To capture the cost implications of various QoS networks, we performed network simulation for the dimensioning of network for different types of QoS and different types of QoS requirements. In the real implementation for this estimation, the bandwidth manager will measure the utilization and other performance and approximate the optimal dimension of the current network load. One reason for using simulation in this study is that there are few end-to-end QoS support networks and their cost data is not available for experimentation which fit our goals. Since we need to control the offered traffic, QoS mechanisms, QoS requirements, and network capacities, the use of simulation is a good choice. For the given optimal dimensions for different QoS requirement of different QoS networks, the bandwidth costs will be assessed using the assumed market value of network interconnection. From this study, the several important cost characteristics such as marginal costs per QoS or bandwidth will be captured. The results of cost assessments will be approximated through proxy opportunity cost function of different QoS networks. The useful cost characteristics for pricing such as marginal costs will be captured through this approximation.
4.2 Demand Models of QoS networks The demand functions can be modeled by capturing utility characteristics for different network services. The demand function we consider in our model captures two different types of utility (price utility and service quality utility). Different types of utility functions are developed for different types of QoS networks. In the network, the service demand can be represented as aggregate offered data rates for the given capacity for the
specific services. The general demand functions can be joint functions of price, service levels, and the utility variables (on price and service) as described as follows:
As it is in the following equation, the network service demand for each PHB classes can be represented as aggregate offered effective data rates for the given price and quality and aggregate number distribution. ? Ri ( pi , si , ki , t ) ? ri max ?1 ? ??
? pi (t ) ? ?? ?? ? pi max ?
? i (t )
?? ? ?1 ? ?? ??
? bi max ? si (t ) ? ?? ?? ? bi max ? wi min ?
? i (t )
? ? (t ) ? ?ki (t )? i ??
where pi(t): price per unit of time and effective kbps for PHB class i pimax: maximum willingness to pay per unit of time and effective kbps for PHB class ? i(t): factor for demand elasticity and convexity on price for PHB class i si(t): currently assigned token priority value of the service for PHB class i bimax: the maximum token value priority value for the best level of PHB class service wimin: the minimum token value priority value for the worst level of PHB class service ? i(t): factor for demand elasticity and convexity on quality for PHB class i ki(t): number of aggregation for PHB class i ? i(t): externality factor of aggregation for PHB class i rimax(t): maximum effective data rate of average individual connection for PHB class i Ri(t): aggregate effective offered data rate for PHB class i
For the different assumptions of the demand elasticity for different PHB classes, we will be using simplified demand function to find the optimal strategies of the bandwidth broker to manage the bandwidth and QoS of DiffServ domain. In the real implementation of this mechanism we would assess input variables such as pimax ,? i(t), bimax , wimin , ? i(t), ki(t), ? i(t), and rimax (t) for the different time of the day and week through the measurement and survey for the service. The revenue function of the DiffServ network will be estimated using this demand function. Notice that pricing
schedule and service level schedules are independent decision variables of DiffServ’s bandwidth broker.
The normalized demand functions on price and quality can be represented as in Figure 4. The demand factors, ? i(t) and ? i(t), can provide the information of the concavity and convexity ( as illustrated with dotted lines in Figure 4) or elasticity (as with solid lines) with different values.
Pi / Pi-max
(B i - Si) / (P i-max -Wi)
Figure 4: Demand Function of Price and Service Quality
Offered Data Rate
4.3 Network Service Pricing Model The pricing of QoS services also plays the key role for determining the economic behavior of individual QoS networks for interconnection. There have been various pricing schemes proposed for an integrated service network, like the Internet. These include priority (service performance differentiation) pricing, congestion spot pricing, and optimal opportunity cost pricing.
Cocchi [3] et al. and Gupta et al. [4] studied the priority pricing methods for networks with multiple service classes with different performance requirements. In this pricing scheme, the price is determined from the network based on the priority of the application requested and associated performance objectives. These studies show that priority based
pricing schemes provide more surplus and profits to the users and networks, respectively, than the flat pricing scheme for the integrated service environment.
In congestion based pricing, the price is set based on the current load and congestion of the network. For example, higher congestion assumes higher demand, so higher price. The congestion pricing was initially proposed by Naor [8] as a way of optimizing the computer usages and applied to a single queuing system in [11]. Mackie-Mason and Varian [7] expanded the idea as a spot price congestion price model for the Internet service access for the demand (willingness to pay) with the form of dynamic auction (multiple level of demand). The frameworks for congestion pricing for more complicated network environments have been further extended recently in [4] and [1].
Differently valued demand and cost characteristics for QoS network services can define optimal QoS pricing schedule where service providers can maximize their profits or maximize the total surplus (consumer surplus and network profits). In our bandwidth management optimization model, we propose an opportunity cost pricing model to be used for different types of PHBs which have different service characteristics within the DiffServ networks. This approach was previously proposed for connection oriented network pricing like ATM by Wang et al.[10]
For the opportunity cost based pricing scheduling for DiffServ networks, the marginal capacity usage increase for different QoS classes and marginal cost increase for unit capacity should be captured over the predefined optimization time. The marginal cost itself as described above should be the pricing schedule which maximizes the total surplus of the networks (user and network) according to the economic theory of welfare.
4.4 Network Resource Management Optimization Model In this subsection, we outline the optimization process that the bandwidth managers of aggregate QoS support network will perform. The optimization problem will be formulated and calculated by the bandwidth manager using the economic models developed in the previous sections. Here we propose the implementation framework for
the optimization process and classify the optimization problems in terms of tasks of the bandwidth managers. Finally we will perform a case study as an application of this optimization on the resource management problems of QoS interconnection model for DiffServ networks. Within each resource management domain, a bandwidth manager program will solve several steps of optimization problems. Within the QoS support domain, each BM (Bandwidth Manager) will act as a decision maker on admission control, service selection, service preferences, service allocation, and pricing strategies. To do these, the BM should be able to estimate current load and performance information within its network. For the neighboring networks, the BM will act as a bandwidth broker which makes decision on connection provisioning, service assignment, admission control and QoS bandwidth exchange rates. For this purpose of exchange, the bandwidth broker may use bandwidth price index from the bandwidth commodity market. The bandwidth brokers will trade spare bandwidth of their networks with neighboring or coexisting networks. Those bandwidth trading can be implemented in conjunction with the adjustment of routing information at the peering interconnection points. The intradomain optimization procedure can be summarized as follows: ? ? Collect and measure the local traffic load of the home domain networks. ? ? Estimate the demand level of each service for each IP bit pipe. ? ? Estimate the opportunity costs of different services for each IP bit pipe. ? ? Schedule the optimal pricing for each service. ? ? Schedule the optimal quality level (priority token) for each priced service. ? ? Develop the service selection preference lists. ? ? Use the selection preference list for the service admission control. ? ? Apply the service level assignment for admitted connections. ? ? New service admission will update local load profile, and the local load profile will be regularly monitored. Initialize the process again.
The inter-domain bandwidth trading is done more at the level of service aggregates of services rather infrequently. ? ? Collect and measure the local traffic load of the home domain networks. ? ? Estimate the demand requesting level of each service for each IP bit pipe.
? ? Estimate the opportunity costs of different services for each IP bit pipe within the domain. ? ? Exchange the query of the available or requiring bandwidth and pricing with neighboring and existing BM. Aggregate level service query are exchanged. ? ? Compare the bandwidth-trading query with the local resource management optimal strategy to check the acceptance of the query. ? ? If the query is an admissible range, consistent with the local resource management strategy, update the service level agreement (SLA) profile for the updated interconnection. ? ? Perform the internal resource allocation optimization for the newly provisioned services with admission control. ? ? New service admission and provisioning will update local load profile, and the local load profile will be regularly monitored. Initialize the process again.
4.5 QoS Interconnection Settlements and Resource Allocation Strategies In the network environment of QoS networks, the absence of settlement may lead to unintended economic distortion among the network providers due to the asymmetry of cross-traffic and heterogeneity of the QoS resource requirement. Interconnection pricing is a way of explicitly motivating to the network providers to provide interconnection for the benefit of indirect network users and consistently maintain the quality of the connection even for transit connections. Therefore, there should be certain financial interconnection settlements required to make the network of QoS networks work with reasonable economic incentives. To evaluate the interconnection settlement, the QoS pricing model mentioned in the previous section should be modeled as a QoS interconnection pricing model. The QoS interconnection pricing model is financial part of QoS interconnection settlement. In addition, the QoS metric (QoS allocation) is the technical part of QoS interconnection. The QoS interconnection settlement should be achieved one of the following general models of settlement in the Internet: ? ? Sender-Keep-All: In Sender-Keep-All model, ISPs keep all subscriber payment without any settlement with other ISPs who participate in routing and delivering
traffic. This is the solution which minimizes the transaction costs of interconnection due to administrative convenience if the QoS of the traffic is not the concern of the public or the resource is abundant or the traffic and QoS symmetry exist. Thus, in such cases, there is no need for QoS traffic metric and pricing in the QoS interconnection. However, in a realistic QoS network, the applications of this model are very limited due to limiting assumptions. ? ? Peer-to-Peer Bilateral: This is an Internet specific model of Sender-Keep-All with assumptions which make the different interconnecting networks peers rather than customers of the network. Such assumptions include ``traffic symmetry, same network size, experience, technology and customer base''. The networks which do not meet these assumptions may be involved in different settlements which are discussed below. In this case, QoS pricing may not be performed for the incentives of the interconnection, however the administration of QoS metric possibly exercised for the sake of fair resource allocation of QoS interconnection. ? ? Hierarchical Bilateral: This is most pervasive interconnection model of today's Internet and it is expected to remain the same in the QoS interconnection of the next generation Internet. In this model, there are remarkable distinctions among interconnecting networks in terms of traffic, network size, experience, technology and customer base mentioned above. Such distinctions will not make the peer-topeer relationship among interconnecting networks any more and change such relationship to customer-provider or resale relationship. The financial and QoS terms and conditions will be the settlement outcomes due to the uneven bargaining strengths of different networks. ? ? Cooperative Administrator: Under the assumption of cooperative incentive among the interconnecting networks, a cooperative administrator can be established and run by interconnecting firms. This cooperative administrator will manage interconnection and QoS allocation for the purpose of cost sharing. This model provides a minimized transaction cost interconnection solution, as
compared to bilateral and third party administrator when the number of interconnection party increases. However, it is a quite limited solution since the full cooperation among the different firms is difficult to achieve and there is much potentiality of discrepancy on QoS allocation and cost sharing among the network providers, especially for the competing networks. ? ? Third Party Administrator: This model involves a neutral paid administrator firm who is not operating a network. The neutral administrator provides the network access points and interconnection administration management services to the network operators. The third party administrator should insure all aspects for fairness of the interconnection to the operator (open access, monitoring the traffic contract, QoS allocation, and pricing). To maintain trust with network operators, the administrator should be able to provide technical means of interconnection information which is clearer to network operators than the information from interconnecting bilateral networks. The efficiency and fairness of the third party administrator will affect network externality positively. This is often called commercial Gigapop which provide QoS attribute translation and associated pricing arrangement for the interconnection for the next generation Internet.
For the above settlement consideration, we will see Hybrid QoS Interconnection as an example of the BM's optimization problems. Each network's inter-domain task strategy will define the settlement scenario of interconnection differently. The differently defined interconnection scenarios will model internal resource management optimization differently. In the following we will present the optimization model for different QoS interconnection scenarios where individual QoS networks will choose network services selectively, including quality level and pricing strategy. The function fi is the marginal cost function from the cost analysis, and the discount functions and volatility functions are considered too. Three settlement scenarios, S-K-A (Sender-Keeps-All, N-C-B (NonCooperative-Bilateral) and C-B (Cooperative-Bilateral) will be considered in this study. S-K-A is the case where no settlement is in place. N-C-B is the case where the price, service and quality selections for the interconnections are done in selfish way by each
different domain. It is consistent with the profit maximization model of previously discussed optimization for individual networks. C-B is the case where cooperative incentive exists for both of the interconnecting networks. These settlement scenario will affect the optimization strategies of both inter-domain and intra-domain operation. The followings are the interconnection optimization model for the bilateral interconnection for different settlement scenarios.
S-K-A: (Sender-Keeps-All)
arg min ? i ,si
? f Re i
i
? ?t
? i (t )dt
i
N-C-B: (Non-Cooperative-Bilateral)
arg max ? i , s i , pi
?[ p ? i
i
f i ]Ri e ? ? t? i (t )dt
C-B: (Cooperative-Bilateral) arg max i , j , si , s j , pi , p j
? ? ?[ p
i
i
? f i ]Ri e ? ? t? i (t ) ? [ p j ? f j ]R j e ? ? t? j (t )dt
j
where: i : PHB class service selection j: PHB class service selection si: quality level selection (token priority value of the service) for PHB class i sj: quality level selection (token priority value of the service) for PHB class j pi: optimal price selection for PHB class i pj: optimal price selection for PHB class j fi: opportunity cost for PHB class i fj: opportunity cost for PHB class j Ri: aggregate demand in effective offered data rate for PHB class i Rj: aggregate demand in effective offered data rate for PHB class j e-? t: discount function with the discount rate of ? ? i(t): volatility function for PHB class i ? j(t): volatility function for PHB class j
Using the above optimization models, we can analyze the different network’s resource management strategies on pricing, service selection and quality selection for different settlement scenarios. In real implementations of resource allocation for the interconnection to DiffServ networks, the bandwidth broker should establish the SLA (service level agreement) with different price and service schedule based on these mechanisms.
5. Optimization Formulation and Numerical Simulation of the Model In order to analyze the economic behavior of different QoS networks and address the questions related to the QoS interconnection, we perform the computer network simulation for the dimensioning and numerical simulation for the economic models further.
First, we modified the computer simulation model used in our previous study [5] to capture the opportunity costs of different PHB classes of DiffServ networks. The base network we simulated is a 5-backbone switch network which is interconnected with DS3 links. We offered average 1600 Erlangs of voice traffic and 15.8 Mbps of data traffic throughput as a maximum offered load of the network to each switch. For voice traffic, we assumed that the traffic is compressed voice and silence suppressed using G729A.
Using the recent traffic data measured by [2], [9], and [6] on the Internet backbone OC-3 trunks, we modeled the integrated service traffic as a cross section of the Internet backbone traffic, and computed the intensity of this traffic relative to voice call demand.
We simulated a simple DiffServ IP network which treats each packet differently based on the priority set in the TOS bytes. We simulated the voice load and data traffic load as EF (Expedite Forwarding) and DF (Default Forwarding) class of the DiffServ network. In a similar way, we monitored the usable bandwidth and the delay for the different relative load of base line traffic load we mentioned above.
The Figures 5 is the opportunity cost trends of the QoS requirement for the different PHBs. The bandwidth opportunity costs are derived from the usable idle bandwidth for different levels of QoS with different QoS requirements.
Figure 5: Usable Bandwidth Measurement for Different PHBs
BW Costs
DiffServ 40 35 30 25 20 15 10 5 0 -5 0
EF DF DF-w
500
1000
1500
2000
Packet Delay (msec)
The usable bandwidth of the EF is measured for different requirement of the 99th percentile packet delay. The usable bandwidth of the DF is measured for different requirement of the mean packet delay. The usable bandwidth of the DF-w is measured for the worst packet delay.
For any fixed capacity interconnection, the maximum usable bandwidth of each PHB will be bounded at least by the usable bandwidth of overengineered network of that PHB QoS requirement. For example, if the EF (5 msec) service can be utilized up to average 30 % of the DS-3 interconnection of overengineering, the offered load of the same PHB still cannot exceed the upper bound even with differentiated services. Therefore, the available bandwidth of interconnection for the high priority will be approximately the same with the entire capacity of the interconnection. Consequently, the opportunity cost of the highest priority will be the function of the total capacity interconnection price divided by the PHB’s achievable average utilization in kbps. Different opportunity costs of different PHBs with different level can be calculated when they are highest priority in the interconnection SLAs. The opportunity cost of the second highest priority will be also dependent on the available capacity of the interconnection. The available capacity for
this second priority will be total capacity times (1 - utilization) of the higher priority PHB. Therefore, in similar way, the opportunity cost of this second priority PHB can be the function of the available interconnection capacity price (total interconnection price * available utilization for the second priority PHB) divided by the total PHB’s achievable average utilization in kbps. This algorithm means that the opportunity cost for the lowest or best effort PHBs opportunity costs will be approaching zero when the interconnection capacity is almost fully utilized by the higher PHB classes. Using above method and data we calculated the DS-3 interconnection opportunity costs for EF-50 msec and DF-500 were calculated in following ways. Assuming the raw DS-3 interconnection price of $54000, the following opportunity costs for different PHB are calculated from the above observation.
The optimization model for the specified example can be expressed in the following forms with the constraints:
arg max i , j , si , s j , pi , p j
?[ p
EF
? f EF ]REF e ? ? t? (t ) ? [ pDF ? f DF ]RDF e ? ? t? (t )dt s.t. fEFREF, fDFRDF ? IC0 fEFREF + fDFRDF ? IC0 fEF ? pEF ? pEF-MAX 0 ? pDF ? pDF-MAX 0 ? REF ? REF-MAX 0 ? RDF ? RDF-MAX REF + RDF ? C
The stated constraints imply the proposed bandwidth management mechanisms and the network characteristics in the following ways. The first constraint says that the individual opportunity costs are limited to quantify the costs which are less than the market value of the interconnection IC0. The second constraints represent the gain of the interconnection due to the differentiation of the service traffic since the IC0 is the cost for
best-effort interconnection data from the current market. The third and fourth constraints state that the selected price schedule from the DiffServ interconnection is bounded with individual opportunity costs and demand price bound. The fifth and sixth constraints represent the bandwidth allowable for each service are constraint with the demand characteristics for the interconnection shown the previous demand model. The last constraint shows the capacity limit of the interconnection which is 45 Mbps in the example case in this section.
Figure 6: Opportunity Costs for PHBs Schedules with Admission Control Opportunity Costs of PHB with Admission Control Opportunity Costs $ per kbps per month
25
20
EF DF
15
10
5
0
0
5 10 15 20 E F A d m i s s i o n C o n t r o l S c h e d u le ( M b p s ) f o r D S - 3 i n t e r c o n n e c t i o n
Using the above opportunity costs for different admission control schedules, we simulated the following base case model, which specifies parameters of demand for different PHBs. We'll use the parameter set and solve the optimization model numerically. Finally, we will perform sensitivity on the some of the major parameters. The following tables summarize the base model parameters and the resulting service schedules for the base DiffServ network. For simplicity, we only consider the price elasticity of the PHB groups here. Therefore, following simplified demand function should be added for the above optimization model. The demand function could be selected in different forms such as exponential forms. We assumed the demand of the EF is much inelastic than DF. No discount rate is assumed for each optimization. The volatility of the network demand is assumed to be the gamma distributed with the mean of 1 and variance 0.1.
? Ri ( pi , t ) ? Ri max ?1 ? ??
? pi (t ) ? ?? ?? ? pi max ?
? i (t )
? ? ??
Table 1: Demand and Network Base Parameters for Different PHB groups Parameters
EF Values
DF Values
Maximum Rate, Ri-max
22 Mbps
45 Mbps
Maximum Price, pi-max
20
1.2
Demand factor, ?
0.9
0.3
54,000
54000
45 Mbps
45 Mbps
0
0
? (0.1, 10)
? (0.1, 10)
I
Market Interconnection Value, IC0 Interconnection Capacity, C Discount rate of ? Volatility function ? i(t)
For the above arbitrary example, the parameters are chosen to represent the practical network situation of the DiffServ network. Unlike the general best-effort interconnection, this QoS interconnection requires fair amount of voice traffic (which is EF) to be transported over the DiffServ network. Assuming the $1800 per month for T1 PSTN connection, we considered the $20 per kbps per month for VIOP would be the price that the last user of the network leaves to the PSTN for the voice service. However, the maximum price for the DF is considered to be bounded with the average price of the general best-effort interconnection because differentiated DF might have more degraded network service quality than the general best-effort network interconnection. The best effort DF is more elastic to the price than the EF in the QoS-interconnection which assumed to be reasonable. With the above parameter values and demand, one can solve the optimization solution of the bandwidth management of the DiffServ network. Following table summarizes the numerical solution for the base case.
Table 2: Numerical Solution of the Base Case Variables Profit Maximizing Price, pi Networks Profit, F Bandwidth Allocation, R i Opportunity Cost Price, p0 Network Revenue, E Bandwidth Allocation, R0
EF Values
DF Values
10.05
0.6
48104.92
675.2
10.16 Mbps
8.44 Mbps
3.08
0.52
52424.68
5418.39
17.02 Mbps
10.39 Mbps
The key observations from the example results are as follows. Note first that the profitmaximizing price of the EF is more deviated from the opportunity cost pricing than the price of DF did. We observed that the profit of the DF service over the opportunity costs were very stable for any prices in the range of $ 0.52 and $ 1.2.
These results are
consistent with the economic theory of profit maximization pricing. High variation from the opportunity costs for the inelastic service EF and no incentives of variation of pricing from the opportunity costs for the elastic service DF in this case. With a profit maximizing pricing schedule, the ratio of the EF price to DF price was 16.75. The comparative ratio for the opportunity cost pricing was only 5.9.
For the given profit
maximization price, the served networks usage of the interconnection capacity is suppressed to 40 % of the utilization which could be adopted the bandwidth broker’s admission control schedule for EF PHB traffic. With opportunity cost pricing, the demand for the interconnection was more than 60% of the utilization of the interconnection capacity. With the profit maximizing pricing, the network service provider could generation additional 90% of the profit in addition to the network opportunity costs of DS-3 interconnection. Notice that the opportunity cost pricing generates the integrated revenue which recovers its opportunity costs of $54,000 with slight additional deviation.
6. Discussion and Future Work In this paper, we developed a framework for the bandwidth management of IntServDiffServ interconnection. The motivations for these interconnection and related
problems were presented at the beginning of the paper. We used the market-based network economic model as the implementation mechanisms for optimizing interconnection policies through the bandwidth management of DiffServ networks. The economic model encompasses cost, demand, pricing and settlement. The theoretical network economic models are developed to characterize different economic variables and properties of QoS network services.
First, we propose to capture some of the important economic cost variables of the network services for the purpose of problem formulation. For example, the bandwidth broker in DiffServ network domain may assess the costs of the individual network services based on the estimation or the measurement of network usage and the market value of the telecommunications transport and interconnection capacity. The estimation of the network usage can be assessed through the information access for the accumulated values of the token priority values which is positively proportional to the admitted traffic load for the specific QoS interconnection service. The individual token priority value is assigned for each individual requesting IntServ’s RSVP flow using RSVP’s token bucket parameters and the DiffServ’s PHB priority policy and provisioning. The market value of the transport capacity can be assessed through the dynamic price information of online bandwidth commodity market such as www.ratexchange.com. or bandwidth broker’s collocation or interconnection price exchange. Therefore, the economic cost assessment we consider is not the real engineering capital costs but the opportunity cost (shadow price) for the fixed capacity network with fixed interconnection link capacity. We used computer simulation to capture the idle usable capacity of the fixed network interconnection link capacity for different QoS requirements, for example different delay variation for EF PHB of DiffServ.
For the extended work of this study, we may consider the multiple bandwidth management trading situation where the individually assessed opportunity costs for different types of PHB groups for different bandwidth management network domains can be represented as the indifference characteristic cost functions when the interconnection between the networks is considered as shown in Figure 7. The
indifference curves for different QoS requirement can be used to define the exchange rates among bandwidth brokers of bandwidth by capturing the slope of indifferent curves.
Net 1 Bandwidth Cost
Figure 7: Bandwidth Cost Indifference Curve Among Bandwidth Brokers
QoS 1 QoS 2 QoS 3
Net 2 Bandwidth Cost
We will further extend this pilot study for various scenarios of the network management and perform the sensitivity analysis for various important network and demand factors. In addition, we will measure the effect on the network welfare including consumer surplus for those various interconnection scenarios. The discount rate and volatility effect on the network interconnection costs and network loads are not varied in this study, therefore the effect on the network bandwidth management for such uncertainty of the market information will be evaluated too in the future study.
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[4] Gupta, A., Stahl, D., and Whinston, A. Priority pricing of integrated services networks. Internet economics (1996), 323--352. [5] Hwang, J., and Weiss, M. Cost/Benefit tradeoff of quality of service mechanisms in integrated service networks. In 27 th Annual Telecommunications Policy Research Conference (1999), TPRC. [6] Internet statistics and metrics analysis: Engineering data and analysis. http://www.caida.org/ISMA/isma9809/report.html September 1998. Workshop Report of ISMA'98. [7] Mackie-Mason, J., and Varian, H. Pricing the internet. Public Access to the Internet (1994). [8] P., N. On the regulation of queue size by levying toss. Econometrica (1969). [9] Thompson, K., Miller, G. J., and Wilder, R. Wide-area internet traffic patterns and characteristics. http://www.vbns.net/presentations/papers/MCItraffic.ps, December 1997. An abridged version appears in IEEE Networks, November/December 1997. [10] Wang, Q., Peha, J., and Sirbu, M. Dynamic pricing of integrated services networks. Presented at the Telecommunications Policy Research Conference, October 1995. [11] Whang, S., and Mendelson, H. Optimal incentive-compatible priority policy for the m/m/1 queue. Operation Research (1990), 870--883.
