Optimal Resource Management in ATM Networks Michael D. Logothetis Wire Communications Laboratory, Electrical and Computer Engineering Dept., University of Patras, 261 10 Patras, Greece. Tel: +30 61 991722 Fax: +30 61 991855 E-mail:
[email protected]
Abstract In the beginning an overview of network management and traffic control in ATM networks is presented, based on the fact that traffic control is distinguished in two levels, the Call-level and the Cell-level control, according to the distinction of ATM traffic in call and cell components, respectively. Afterwards, the paper concentrates on the Call-level and mainly on traffic controls which effectively manage the network resources (bandwidth) and whose the performance is drastically influenced by the bandwidth capacities of the transmission links of the networks. Especially, the impact of Virtual Path Bandwidth (VPB) control on ATM network performance is discussed. Furthermore, the optimal VPB control is presented, which minimizes the worst Call Blocking Probability of all Virtual Paths (VP) of the network. A centralized VPB controller can readily rearrange the VP bandwidth of an ATM network having an appropriate architecture, composed of ATM Cross-Connect systems. The controller solves a large network optimization problem by a rigorous analytical procedure. The optimization model comprises bandwidth distribution schemes assuring network reliability. The demand for reliability requires considerably larger bandwidth to be installed in the backbone network and, therefore, optimal VPB control becomes essential. The procedure for optimal VPB allocation is clarified, step by step, in a tutorial application example. In a more realistic example, the optimal VPB control is applied on a model ATM network. Keywords: ATM, Traffic Control, Virtual Path, Bandwidth Control, Optimization and Reliability.
1.
Introduction
During the last decade, the steadily increasing volume and the variability of telecom traffic have dictated important innovations for the resource/traffic management of telecommunication networks. The role of bandwidth management in quality and network-reliability assurance is upgraded in the expected environment of broadband integrated services digital network (B-ISDN) [1,2]. In the near future, B-ISDN will convey traffic of several service-classes with very different requirements in bandwidth (bits per second) and quality of service (QOS) per call, while reliable traffic demand forecasting for these services seems to be impossible. Moreover, different traffic streams are mixed and commonly share an end-to-end link. This wide variety of service-classes renders the resource management more difficult but also more important. To simplify the study this paper concerns service-classes with strict QOS requirements (Table 1). B-ISDN gets under way thanks to the asynchronous transfer mode (ATM) transmission and switching technique which offers an inherent flexibility in traffic management by "virtualizing" the network resources and especially by deploying the VP concept. Simple but efficient traffic management can be established to ATM networks by handling the different ATM network services in a common way and assigning them the required network resources adaptively [3,4].
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In ATM networks two levels of traffic control, the Call level and the Cell level control, are present, which correspond to the distinction of traffic in call and cell components, respectively (Fig. 1) [5,6]. Each Call consists of a stream of a fixed-size (53 bytes) piece of information transmitted in ATM network after call connection. Concentrating on the Call-level management, this involves mainly Congestion control, Virtual Path Bandwidth control, Virtual Channel Routing control (dynamic routing) and Bandwidth (trunk) Reservation control. The Call-level network performance is evaluated by the Call Blocking Probability (CBP). T r a f fic C o n t r o l in A T M N e t w o r k s VPB
D y n a m ic R o u t in g
B a n d w id th R e s e r v a t io n
C o n g e s t io n C o n tro l
C a ll L e v e l
C e ll L e v e l
CAC
T r a f f ic S h a p in g
UPC
B u f f e r in g m anagem ent
Figure 1: Layered structure of traffic control in ATM networks. VPB control is a medium- or long-term network control (network planning). VPB control in cooperation with a bandwidth reservation control scheme changes the installed bandwidth in the VPs according to the offered traffic so as to improve the global performance of the network, under constraints posed by the transmission links capacities [7,8,9]. The resultant distribution of the totally installed bandwidth in the network to the VPs is the VPB allocation. VPB allocation can assure network reliability in a high degree. A reliable bandwidth allocation is considered, by enforcing the bandwidth to be distributed at least in two VPs of every switching pair (end-to-end link). To ensure network reliability, however, we need to install an enormous amount of bandwidth in the transmission links, in comparison to an unreliable network, whereas due to traffic variations (even long term) a lot of bandwidth remains unused. Therefore, the optimal VPB control becomes essential. This paper is concentrated on the optimal VPB allocation, which is achieved through a network optimization model [9,7]. Many heuristic and efficient algorithms to solve a network optimization problem have been proposed for ATM networks [3,10,11,12,13], whereas path bandwidth management has been considered in synchronous transfer mode (STM) networks too [14,15,16,17,18]. All the proposed algorithms, however, lead to sub-optimal or practically optimal results. For a refined network study and for evaluation of the various bandwidth control schemes, it is necessary to apply analytical algorithms, whereby we can obtain accurate results even with much consumption of computer memory and CPU-time.
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The network optimization problem is composed of the offered traffic, the topology of the network, the routing table comprising all the VPs, the installed bandwidth in the transmission links, the demand for reliability and an optimization criterion. The criterion of minimizing the worst CBP of the whole network has been adopted. The problem is formulated as a non-linear programming optimization problem, where the objective function is to minimize the worst CBP of the whole network under the following two main constraints: A. Bandwidth capacity of the transmission links. B. Reliability constraints. A rigorous and analytical procedure is presented which leads to the exact (optimal) solution of the network optimization problem [9]. Optimal VPB control can be applied for network planning [19]. In this paper, the term network planning means the planning of the extensions of the bandwidth of the VPs and, consequently, of the capacity of the transmission links of an existing ATM network. To meet the traffic increase and variation, the VPs of the network are sized periodically on the basis of traffic forecasts or on the measured grade-of-service. In both cases, however, some VPs are undersized and other oversized, because errors are obviously inevitable. Eventually, undersized VPs are excessively congested before the end of the planning period, while in the mean time oversized VPs have excess bandwidth-capacity. To deal with this specific network-planning problem, the "performance-oriented management" concept is adopted, described in reference [20], as the most appropriate network planning strategy under demand uncertainty. According to this concept, the performance of the VPs is evaluated periodically by measuring the CBP (for each service-class) and when the performance deteriorates below a standard level, additional network resources are assigned adaptively to the VPs. To achieve the performance-oriented management a flexible mechanism is required for assigning network resources in timely manner. Fortunately, the ATM technology inherently gives us the possibility not only to assign the network resources adaptively, but also, to rearrange dynamically the already installed resources. In reference [20] the performance-oriented management is combined with dynamic routing in order to save investment in the network life cycle. However, since by dynamic routing the problem of re-sizing of VPs is not faced but simply postponed, performance-oriented management combined with VPB Control and the incorporation of bandwidth (trunk) reservation control, constitute a more efficient scheme for network planning. Two application examples are presented in order to clarify and reveal the efficiency of VBP control in resource management. In the first example, the optimal VPB Control is applied on a small network of three nodes, for tutorial purposes. In the second example, the optimal VPB Control is applied on an eight-node ATM network of realistic dimensions, supporting two serviceclasses. The organization of this paper is as follows: Section 2 presents in brief the ATM serviceclasses and discusses the ATM network/traffic management from the viewpoint of quality assurance. The two layering (Call-level and Cell-level) architecture for traffic management is presented. The Cell-level traffic management and the traffic controls of the Call-level traffic management are discussed briefly, in subsection 2.1 and subsection 2.2, respectively. Section 3 concentrates on the Call-level traffic controls dealt with the bandwidth capacities of the transmission links. The VPB control/allocation is presented in more detail, in subsection 3.1, since is the main subject of this paper. In subsection 3.2 the VPB control is compared to the dynamic routing control which is the conventional Call-level traffic control and to the Bandwidth
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Reservation control. The optimal VPB allocation obtained through a network optimization model is presented in section 4. Subsection 4.1 presents an appropriate ATM network architecture for resource/bandwidth management. Network reliability is discussed in subsection 4.2, from the viewpoint of bandwidth management. Subsection 4.3 presents the definition of the network optimization model as a non-linear programming optimization problem. Its solution is presented in subsection 4.4. How the optimal VPB control can be applied for network planning is presented in section 5. Section 6 presents two application examples of VPB control in ATM networks. The tutorial example is presented in subsection 6.1 and the second example, which reveals the performance of VPB control in realistic ATM networks, in subsection 6.2. As a conclusion, the main points of this paper are summarized in section 7.
2.
Traffic management in ATM networks
The ATM Forum has classified the ATM layer service-classes as summarized in Table 1 [21,22]. The first column of Table 1 presents the ATM service-classes, the second column gives an example of each service-class, the third column shows the traffic descriptor used at call setup and the last column contains the specified QOS parameters for each service class. One can notice service-classes with strict QOS requirements (CBR/VBR) and service-classes without strict or not at all QOS requirements (ABR/UBR). Service Example Class CBR Telephony VBR Real-time Video service VBR Non Real-time Banking transactions ABR Distributed file service UBR File transfer (background job) The following abbreviations are used: CBR for Constant Bit Rate VBR for Variable Bit Rate ABR for Available Bit Rate UBR for Unspecified Bit Rate
p-t-p max
Table 1:
for for
peak-to-peak maximum
Traffic Descriptor QOS Parameters PCR CLR, max CTD, p-t-p CDV PCR, SCR, MBS CLR, max CTD, p-t-p CDV PCR, SCR, MBS CLR, mean CTD PCR, MCR CLR PCR Not Specified
PCR SCR MCR MBS CLR CTD CDV
for for for for for for for
Peak Cell Rate Sustainable Cell Rate Minimum Cell Rate Maximum Burst Size Cell Loss Rate Cell Transfer Delay Cell Delay Variation
ATM service classes – Characteristics.
Traffic management is considered as a series of traffic handling procedures necessary for proper network operation and quality of service assurance. Three main areas of traffic management are distinguished: a) Network planning. b) Traffic control. c) Traffic & QOS measurements.
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Network planning is a long-term traffic management and aims at an adequate topological network design as well as at a proper network dimension (resource allocation) so as to meet the best possible QOS specifications by taking into account mainly economic factors (available capital investments, etc.). An example of the network-planning subject for an existing network is the planning of the extensions of the bandwidth-capacities of the transmission links of the network. Traffic control is a rather medium- or short-term control and aims at achieving the best possible QOS for certain (given) network resources. QOS often decreases when an imbalance exists between the network resources and the offered traffic. To improve the QOS a first action (short-term control) is taken by a traffic control mechanism in order to remove the cause, while a final action (long-term) is taken by the network planning. Traffic measurements (offered and carried traffic) and measurements of QOS are important, because they are necessary for the traffic control and network planning. Real-time traffic monitoring is necessary in changing the traffic control parameters adaptively so as to improve the flexibility and reliability of the traffic control. Long-term measurements of QOS of the network leads the network planning to timely assignment of the network resources. The subjects of the traffic control are presented below, according to the layering structure of traffic in ATM networks. As it is illustrated in figure 1, the main objectives of the Call-level traffic controls and the Cell-level traffic controls are the calls and the cells, respectively. The QOS index of the Cell-level traffic management is expressed by the cell-loss probability (cell loss rate, CLR) and the CTD, whereas the QOS index of the Call-level traffic management is expressed by the CBP. The subjects (functions) of the Cell-level traffic controls are buffering management, usage parameter control, traffic shaping, and connection (call) admission control. The Call-level traffic controls include the following functions: call congestion control, bandwidth (trunk) reservation control, VPB control and dynamic routing. Call admission control is also related to the Call-level traffic controls. Concerning VP bandwidth dimensioning (Call- and Cell-level) and buffering dimensioning (Cell-level) are subjects of the network planning. 2.1
Cell-level traffic control
Cell-level traffic control is responsible for the Cell-level QOS assurance and comprises the following specific controls (Fig. 1): a)
Buffering management (Priority Control) ATM-cells (traffic streams) with different QOS requirements will be mixed and commonly share a VP. The most stringent requirements of these cells must be satisfied if they would be handled in the same way. This would lead to excess QOS specifications, which in turn lead to lower traffic throughput. Buffering management control assigns a higher buffer-usage priority to cells with stringent QOS requirements so as to achieve a higher traffic throughput. Connection Admission Control (CAC) When a call set-up request arrives at an ATM network, the ATM switches have to decide whether to establish a virtual channel/path (VC/VP) connection or reject the call request. A connection request is accepted only when sufficient resources are available to establish the connection through the whole network at the required QOS and to maintain the agreed QOS of existing connections.
b)
6
c)
Usage and Network Parameter Control (Traffic Policing) Usage parameter control (UPC) is performed at the input port of ATM switches in the UNI (user-to-network interface), whereas network parameter control (NPC) is performed at a NNI (network-to-network interface) to ensure that traffic generated by a user is within the negotiated contract. When violations are detected, UPC or NPC discards all violating cells or places tags on them by setting the cell loss priority (CLP) bit to 1 in the header of the ATM-cells. For CBR traffic, a single leaky bucket is required to perform traffic policing, since CBR traffic uses a constant PCR parameter in its network contract. Traffic policing for VBR traffic utilizes two leaky buckets to monitor both the SCR over a defined period of time and the PCR used by the connection. If either of these parameters is violated, the ATM switch may discard the cell or mark it as non-conforming. d)
Traffic Shaping For most VBR sources, cells are generated at the peak rate during the active period, while no cells are transmitted during the silent period. Therefore, it is possible to reduce the peak rate by buffering cells before they enter the network so that the departure rate of the queue is less than the peak arrival rates of the cells. This is called traffic shaping and can be done at the source equipment or at the network access point.
2.2
Call-level traffic control
Call-level traffic control is responsible for the Call-level QOS assurance and comprises the following traffic controls (Fig. 1): a)
Congestion control When many call set-up requests arrive (congest) at a specific ATM switch, it is probable that not all of them will be accepted. Nevertheless, all the calls need a processing offered by the ATM switch. Due to this processing of even unsuccessful calls the performance of the switch deteriorates. To avoid this phenomenon, called congestion, the congestion control restricts the number of call set-up requests when the number of arriving calls exceeds the switching capacity of the destination switch. b)
Bandwidth (trunk) reservation control In ATM networks cells of different service-classes, which have different bandwidth requirements per call are integrated and commonly share a VP. Therefore, the CBP of service-classes with higher bandwidth requirements becomes worse than that of service-classes requiring lower bandwidth. To decrease this imbalance of the CBP, the bandwidth reservation control reserves some fraction of the VP bandwidth to benefit the high-speed calls. c)
Virtual Channel Routing control The Virtual Channel Routing control control, also known as dynamic routing control, monitors the traffic flow in the transmission links of the network and selects the least loaded route of virtual circuit to convey a call. The CBP met in the transmission links as well as the end-to-end CBP of the switching pairs are improved. d) Virtual Path Bandwidth control
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The VPB control changes the installed bandwidth in the VPs, according to the offered traffic variation in order to eliminate the imbalance between the VP bandwidth and the offered traffic, improving in this way the end-to-end CBP of the switching pairs of the network.
3.
Traffic controls and transmission links
In this section, the study of traffic controls is concentrated on controls, which drastically influence the network resources and the global performance of an ATM network under constraints posed by the bandwidth capacities of the transmission links. Since congestion control deals with traffic congestion that emerges in each ATM switch, this control is excluded. VPB control is the main control strongly related to the transmission links capacities as well as Dynamic Routing and bandwidth reservation control, which is presented comparatively to the VPB control.
3.1
VPB control/allocation
Telecommunication networks are designed to convey the traffic of all switching pairs so as to meet a pre-described QOS. Due to traffic variations from hour to hour the traffic load on some switching pairs is below the forecasted value and free bandwidth results. On the other hand, overloads occurring at the same time on other switching pairs cannot use the free bandwidth of the network, if it is not possible to transfer the surplus bandwidth towards the congested switching pairs. This is the work of VPB control. It reallocates the bandwidth of the VPs according to the offered traffic so as to improve the global performance of the network, under constraints posed by the transmission links capacities. The resultant distribution of the totally installed bandwidth to the VPs is the VPB allocation. Figure 2 illustrates the VPB control. It shows a small network of three ATM switches (ATM-SW) which are interconnected through one Cross-Connect System (ATM-XC). Suppose that this network has been designed perfectly and that at the time of installation it satisfies the design Call-level QOS of 1% (end-to-end CBP). As time goes by, however, traffic changes and in one VP the CBP is high while in other VPs the blocking remains low. To improve this network status, a VPB controller changes the initial bandwidth allocation in the network so as to reduce the maximum CBP of the network. To rearrange the VP bandwidth dynamically the following types of VPB control schemes have been proposed: a) b) c) d)
Very Short-term control schemes based on the information of the concurrent connections in the VPs [3], with control interval less than 5 min. Short-term control schemes based on the blocking measurements taken during the control interval, which ranges from several minutes to few hours [11]. Long-term control schemes based on traffic prediction with control interval ranging from a few hours to a few days [13]. Medium-term VPB control based on traffic measurements, with control interval ranging from several minutes to few hours [23]. The Very Short-term and the Short-term control must be distributed control schemes in
8
order to respond fast to sharp traffic fluctuations and absorb them. To achieve this, they need very simple computations. They could ignore the traffic characteristics of service-classes [3], which is an important advantage in the B-ISDN environment. The Very-Short-term control achieves an optimal network performance. The implementation, however, of this control scheme is very difficult and, therefore, it is only of theoretical value. A large number of control steps is needed especially when the traffic volume is large. The Short-term control schemes are easier implemented but they lack optimality.
Figure 2:
Virtual Path Bandwidth Control
On the other hand, the Long-term control is a centralized control where the controller aims at an optimal network performance in the control interval by solving a large network optimization problem. However, the controller is based on the prediction of the offered traffic, which is a time consuming task, though it is not possible to be accurate. Therefore, the importance of the achieved optimality is weakened. The main advantage of the Long-term control schemes is that they can easily be implemented, because VP bandwidth is rearranged only a few times per day, at most. The Medium-term VPB control scheme reconciles the advantages and disadvantages of the Short-term and Long-term control schemes. The controller must be a centralized one in order to optimize the network performance globally within its control interval. The control interval must be rather short in order to respond satisfactorily to medium-term traffic fluctuations. Short-term traffic fluctuations could be absorbed by the implementation of Dynamic Routing in a further stage. To achieve this Medium-term VPB control, the controller is based on on-line measurements of the offered traffic. The impact of on-line traffic measurements on control schemes has already been examined in [24,25] for the STM environment and adaptive or dynamic routing control. 3.2
VPB control versus Dynamic Routing and Bandwidth Reservation Control
9
Dynamic Routing selects the least loaded path to convey a call under constraints posed by the VPB distribution to the VPs (VPB allocation), which produced by the VPB control. Figure 3 illustrates the Dynamic Routing, similarly to figure 2.
Dynamic Routing
Dynamic Routing
Figure 3:
Virtual Channel Routing Control (Dynamic Routing)
VPB control competes with Dynamic Routing in efficiency. A main advantage of Dynamic Routing is the easy implementation. It has a very short control interval, in the order of a few seconds (it can act for each call). On the contrary, the minimum control interval of VPB control is in the order of several minutes, due to the required time of bandwidth rearrangement (BRT), because of the existing connections at the time point of bandwidth rearrangement [26,8]. Therefore, Dynamic Routing responses faster than VPB control to absorb the traffic fluctuations. Nevertheless, the time-response of VPB control is satisfactory [23]. Regarding the efficiency of the two controls in the improvement of the call-level QOS (CBP), it has been observed that Dynamic Routing is very effective when the traffic fluctuation rate is small. While VPB control performs best when this rate is large or when the traffic load among the switching pairs is very different [27,28]. Since the latter cases appear in most practical situations, VPB control is more important than Dynamic Routing. Moreover, VPB control does not prevent the coexistence of Dynamic Routing. The successive application of VPB and Dynamic Routing, called Cooperative control, achieves further improvements in network performance [29]. The bandwidth reservation control aims at guaranteeing the grade-of-service requirement of each service-class of the network by reserving some fraction of the free bandwidth of a commonly shared VP for the service-classes which require larger bandwidth. Very frequently, bandwidth reservation is considered together with the VPB control, because the objectives of the two controls are in harmony, as it is explained in section 4.3. The VPB controller takes into account the
10
bandwidth reservation scheme in every bandwidth change that it performs.
4.
Optimal VPB Allocation
The optimal VPB allocation results from the optimal VPB control through a network optimization model. For a refined network study and for evaluation of the various bandwidth control schemes, it is necessary to apply analytical algorithms whereby accurate results are obtained even with much consumption of computer memory and CPU-time. In the following, first an appropriate ATM network architecture for bandwidth management is presented, second, the network reliability is discussed from the bandwidth management point of view, third, the optimization problem is defined and, fourth, its analytical solution is given.
4.1
Network Architecture
ATM-network architecture is considered in which each ATM-SW is accompanied by an ATM-XC system. The ATM-XCs are interconnected by a ring transmission line and compose the backbone network (Fig. 4) [30]. This ATM-network architecture is similar to an existing STM-network architecture where there are digital cross-connect systems (DCS) instead of ATMXCs [31]. It has the advantage of simplicity and offers higher transmission line utilization [32,33]. It is worth mentioning that other network architectures could be considered as well, without important changes in the modeling of the optimization problem.
ATM Network Architecture
Virtual Path Connections
VPB Controller
Figure 4: ATM network architecture.
Figure 5: VP connections in ATM network.
Thanks to the Virtual Path (VP) concept, the traffic management by reallocating the established bandwidth of the paths (VPB management) according to the traffic variations becomes favorable in ATM networks. The concept of VP, whereby two ATM- SWs face only the direct logical (imaginary) link (VP) between them, makes the structure of the backbone network transparent to the ATM-SW pairs. This is due to flexibility of the ATM-XCs to provide the
11
required bandwidth in the end-to-end links of the ATM-SWs. Therefore, from the VPB management point of view, the whole ATM network is equivalent with a meshed network in which only the direct links are used (Fig. 5). The transmission links are assumed bi-directional. A connection between ATM-SWs is established via any available path that has been registered in a table, called Routing Table (RT). Under the consideration of this study the route of a path between ATM-SWs passes through ATM-XCs only. This implies that the total amount of the buffer memory in the ATM-SWs should be involved into the constraint part of the optimization procedure, as it is an existing problem. However, it is not taken into consideration to reduce the problem complexity. In the backbone network with a basic structure of Fig. 4, two parts can be distinguished, in order to make the network study easier. The part of the network composed of the ATM-SWs and their direct connection to ATM-XCs, called outer network, and the part of the network composed of the interconnected ATM-XCs, called inner network. The VPB controller is located at an administrative center (centralized controller). It communicates with the ATM-SWs to collect the measurements of carried traffic and blocking during its control interval. Based on these measurements, it calculates the offered traffic. From the offered traffic, the installed bandwidth in the transmission links and the VPs listed in the RT, the VPB controller determines the distribution of the bandwidth to the VPs, by solving a large network optimization model. Then, it updates the data relevant to the VP bandwidth in the ATM-SWs. The realization of the produced VPB allocation is executed by the ATM-SWs simultaneously, after a delay due to the BRT, because of the existing call-connections at the time point of bandwidth rearrangement. The ATM-SWs increase, or decrease the number of cells which have a specific Virtual Path Identifier [5] when the bandwidth of this VP is increased or decreased, accordingly. It is worth mentioning that, no communication between the VPB controller and the ATM-CXs is required.
4.2
Network Reliability
Reliable network under the consideration of bandwidth management means that in every switching pair if a transmission link failure occurs, bandwidth still remains. A reliability degree is the amount of the remaining bandwidth and the way it is distributed. Network reliability can be resulted by several schemes of bandwidth distribution to paths. As an example the following two schemes can be considered. i) In a first scheme, we assume that for every pair of switches p at least two paths (VPs) exist between them and we enforce a certain percentage gp of the total bandwidth Vp to be allocated to the shortest path. Logical values for gp are in the range of 50% (most reliable) to 75% (less reliable). Although values of gp in the range of 75% to 100% are problematic from the reliability point of view, they are permitted. The value gp=100% means that there is no reliability on bandwidth allocation because the total bandwidth being assigned to each switching pair is allocated to only one path. The certain percentage gp of the bandwidth which is allocated to the shortest path could be the same for all switching pairs (i.e. gp=g) or could be fixed according to the degree of reliability we want to ensure for each switching pair individually. For instance, in order to guarantee best reliability between the switches A and B, gp is set 50%, while between the switches
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A and C gp might be 75%. ii) In a second scheme, we enforce the bandwidth to be distributed to the paths so that the allocated bandwidth to each path r becomes not less than a specific value qr. Again, this value could be the same for all the paths (VPs) of the network or could be specialized as in the first scheme, so long as these specific values satisfy the constraints posed by the installed bandwidth in the transmission links. The value qr=0 is also permitted. The first scheme is preferable because the bandwidth allocation is clearly described.
Network Reliability
Figure 6:
4.3
Network reliability from the VPB management point of view.
Definition of the Optimization Problem To set up the optimization problem mathematically the following notations are introduced:
S P R * R r Rp Rs Cs L Rl Cl Wr Ap Bp
Set of ATM-SWs. Set of ATM-SW pairs. Set of all paths between all ATM-SW pairs (listed in Routing Table). Set of the shortest-paths for all ATM-SW pairs ( R * ⊆ R ). Set of transmission links (sequence of nodes) defining a route r of a path ( r ∈ R ). Set of available paths assigned to the ATM-SW pair p, ( p∈P ). ( s ∈ S ). Set of paths where the ATM-SW s is either source or destination node Installed bandwidth between the ATM-SW s and its accompanied ATM-XC ( s∈S ). Set of bi-directional transmission links of the "inner" network. Set of paths, which utilize the transmission link l. Installed bandwidth to transmission link l, ( l ∈ L ). Bandwidth occupied by a path r between ATM-SWs (Decision variables), ( r ∈ R ). Traffic offered to ATM-SW pair p, ( p ∈ P ). Call Blocking Probability for ATM-SW pair p.
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Vp gp
Total Virtual Path Bandwidth of the switching pair p. Percentage for definition of a reliability demand according to the reliability scheme (i), mentioned in section 4.2, ( p ∈ P ). Bandwidth for definition of a reliability demand according to the reliability scheme (ii), qr mentioned in section 4.2, ( r ∈ R ). = ∑ Wr The Cs is determined at the design phase of the network as: C s
r ∈Rs
The Cl is determined at the design phase of the network as:
∑W
Cl =
r
r ∈ Rl
The Virtual Path Bandwidth (VPB) of ATM-SW pair p, Vp, is the summation of the bandwidth occupied by all paths established for the ATM-SW pair p:
V p = ∑ Wr r ∈Rp
The optimization problem is formulated as mathematical integer programming problem with the following linear constraints and the non-linear objective function: CONSTRAINTS: A.
Due to the limited capacities of the ATM-SWs (outer network - outer constraints):
∑
W r ≤ Cs
for all s ∈ S
r ∈ Rs
B.
Due to the limited bandwidth of the transmission links (inner network - inner constraints):
∑
r ∈ R
C.
W
r
≤ C
for
l
l ∈ L
all
l
Due to demand for reliability (according to the two bandwidth distribution schemes):
i ) W r= g pV
p
for all r ∈ R * , p ∈ P o r
ii ) W D.
r
≥ qr
for all r ∈ R
Concerning the decision variables:
n
r
: non
W negative
r
= nrW integer,
unit
≥ 0 W
unit
: VPB
unit
Remarks: i. The term outer and inner constraints for the Cs and Cl, respectively, are introduced due to their different influence on the VPB allocation. If the reason of the worst CBP is the capacity of a
14
transmission link (inner constraint) it is easy to improve the performance of the network, by re-routing traffic through alternative routes and avoiding the congested link. However, if the reason is the capacity of an ATM-SW (outer constraint), this possibility does not exist. So, the worst CBP in case that it is only due to the outer constraints becomes independent of the configuration and the topology of the inner network. ii. In order for the reliability demand to be meaningful, we must assure that between ATM* ⊂ R. R SWs at least two paths are registered in the RT, that is iii. Not only the decision variables Wr but every notation which expresses bandwidth (Cs, Cl, gpVp and qr) must be an integer multiple of the Wunit. OBJECTIVE FUNCTION
max of B p = G ( V p , A p ) ⇒ to be minimized where G stands for the function giving the CBP from the offered traffic Ap and the available bandwidth Vp of the ATM-SW pair p. In the STM environment where only one service-class exists, G is the Erlang B-Formula:
Bp=
A Vp p / V p ! V
p
∑
A kp
/ k!
k =0
Whereas, in the environment of ATM networks where at least two service-classes are assumed sharing a VP equally, the calculation of CBP can be done by using the recurrent formula given in Ref. [34,35]:
1 1 G(i) = i
for i = 1
K
∑
a c k b c k G( i - b c k ) for i = 1,..., V
p
(1)
k=1
0
otherwise
where K is the number of service-classes serviced by the ATM network, bck is the required bandwidth per call of the service-class ck and ack is the offered traffic of the service class ck to the switching pair p, that is, Ap is a K-size array with elements the ack's. Bp is a K-size array, too. The Call Blocking Probability Bpck of the ATM-SW pair p for the service-class ck, is defined as: bck - 1
B
pc
k
=
∑
j=1
G
-1
G(
V
p
- j ), where
V
p
G = ∑
G(i)
(2)
i =1
In the above formula, bandwidth (trunk) reservation schemes are not incorporated.
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According to the trunk (bandwidth) reservation concept [36], calls of service class ck are refused for service when less than t(ck) bandwidth units remain available in the VP. By selecting properly the numbers t(ck), it is possible to meet the same grade of service among the service classes and so, the worst CBP of the whole network can be improved. To incorporate the Bandwidth Reservation control to VPB control, a good approach is found in Ref. [37]. For calculation of CBP, the following modifications are introduced to the expression (1) and (2). The (1) must be modified for i = 1,...,Vp as: G( i ) =
where
D ck(
1 i
K
∑a
i - b )= ck
ck
D ck(
k=1
{
bck
0
i -b )G ck
for i ≤ V - t( c ) for i > V - t( c ) p
(3)
k
p
k
And the (2), because of the upper limit of the summation, as: By the above approximation, the accuracy of CBP calculation is satisfactory, especially bck + t ( ck ) - 1
B pc k =
∑
G -1 G ( V
p
- j )
(4)
j= 1
when the difference of holding-times of the service classes is small [10]. The formulas for calculating CBP in ATM networks are perfectly fixed for CBR serviceclasses. For VBR service-classes the constant traffic load required by the above formulas may correspond to the SCR parameter or to the notion of effective bit rate (equivalent bandwidth) [38, 6]. However, for the rest service-classes of Table 1 (ABR/UBR), the CBP calculation is an open problem since even the notion of blocking has to be reconsidered [39].
4.4
Optimal Solution
The network optimization problem has been formulated as a non-linear integerprogramming problem. Obviously, the main difficulty in its solution consists in the non-linearity of the objective function. Besides, a difficulty arises from the constraints set C, in the first case of demand for reliability where the right-hand-side values are not constant, as they are in all the other constraints. One more difficulty arises from the demand for integer values for the decision values. To solve the above model analytically the analytical method proposed and proved by Prof. M. Akimaru [18] is followed in general. In the following, it is described how this method is used to overcome the above difficulties and achieve the optimal solution to the present optimization problem; that is, how the bandwidth allocation that minimizes the network's worst CBP is defined. The following approach transforms the non-linear optimization model to a succession of linear integer programming models, in four steps: Step 1: Calculate the initial worst and minimum CBP of the network xmax and xmin respectively,
16
using the function G and based on the initial bandwidth allocation and the traffic demand matrix (it is valid to assume that initially xmax=1 and xmin=0). Step 2: Define a new improved worst CBP as: xnew=(xmax+xmin)/2. Step 3: Find out whether the value xnew can stand for the worst CBP or not, by the following way: * With the aid of a function (let us call it G ) which determines bandwidth from the offered traffic and a given grade of service, calculate the Vp based on Ap and using as gradeof-service the xnew for all p∈ P . * The bandwidth Vp is calculated through G so as to be an integer multiple of Wunit. Because of the constraint set D and the third remark, above, the integer multiples of Wunit are referred in the following by using brackets, i.e.: [Vp] stands for the integer value Vp/Wunit, [Wr] for nr. Distribute all Vp's to the VPs (i.e. define Wr) under the constraints posed by the installed bandwidth to the transmission links (constraint sets A and B) and according to the reliability scheme (constraint set C, i or ii). The difficulty arisen from the constraint set C (i) does not exist any more, because the Vp has been defined (gp is parameter). So, the variables Wr can be defined through the solution of the following set of equations: ! If Ws stands for the possible free bandwidth between the ATM-SW s and its corresponding ATM-XC, then according to constraint set A,
∑
for all s ∈ S
[ W r ] + [ W s ] = [ Cs ]
r ∈ Rs
! If Wl stands for the possible free bandwidth of transmission link l, then, according to constraint set B,
∑
[ W r ] + [ W l ] = [ Cl ]
for all l ∈ L
r ∈ Rl
!
Constraint set assuring the grade-of-service xnew
∑
r∈ R
[ W
r
] = [ V
p
]
for all
p∈ P
p
! Introducing the variable Wqr which expresses the surplus bandwidth for path r over the demanded value of qr, then for the constraint sets C,
i ) [ W
r
] = [ g pV
p
]
for all r ∈ R * , p ∈ P
o r ii ) [ W !
r
Furthermore,
] -[ W
qr
] = [ qr ]
for all r ∈ R
17
[ W
s
] ≥ 0, [ W
l
] ≥ 0, [ W
qr
] ≥ 0, [ W
r
] ≥ 0 (integers)
To solve this set of equations, it is considered as the constraint part of an optimization problem with a linear objective function, which is artificially introduced:
∑
W
r
⇒
to
be
maximized
r ∈ R
Thus, a linear integer-programming problem results which can be solved by classic integer programming techniques. Due to inconvenience of the commercial software packages which support optimization problems with integer stipulations, an iterative algorithm is proposed to be implemented in FORTRAN, based on the well known Simplex method. This is the "primal cutting-plane" algorithm [40]. It guarantees convergence and satisfies throughout (in every iteration) the linear restrictions and the integer stipulations. In addition, the computational technique of Big M method [40] is applied to ensure the equalities in the constraint sets which assure the grade-of-service xnew and the first scheme for network reliability. If the so formulated integer programming model has a feasible solution it means that all Vp's are distributed to the paths and xnew can stand for the new worst CBP; then put xmax = xnew. Otherwise put xmin = xnew. Step 4: Repeat the procedure from the second step until the difference xmax-xmin becomes equal or less than an error e which expresses the accuracy by which we want to estimate the network's worst CBPs (e=0 is valid). Concisely, this algorithm is presented in the flow-chart of Fig. 7. A remaining problem in solving such a model is the huge computer memory that is required for large networks. For a ring 2 type network of N ATM-SWs (Fig. 4), to set up the optimization procedure, N constraint equations and 2N(N-1) variables are required. Regarding the CPU-time, setting properly the initial values of xmax and xmin, considerable time could be saved if the worst CBP could be estimated approximately. Start
Start
Initiate Xmax Xmin
GOS,Xmax,Xmin Xnew=(Xmax+ Xnew)/2
Xnew=(Xmax+ Xnew)/2 Xmax-Xmin>e ? Stop Xmin=Xnew
Xmax-Xmin>e ?
Vp=G*(Xnew,Ap) Distribute Vp to VPs Under the constraint sets Succeeded ?
Stop
Xmax=Xnew
Figure 7:Flow-chart of the optimization procedure.
Xmin=Xnew
If VP grade-of-service >GoS then Vp=G*(Xnew,Ap) else Vp=G*(GOS,Ap) Distribute Vp to VPs Under the constraint sets Succeeded ?
Xmax=Xnew
Figure 8: Flow-chart of the network planning optimization procedure.
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5.
Network Planning Based on VPB Management
Let us assume that the bandwidth, which can be installed in the network at any instant of the planning horizon, is known and depends only on financial reasons. Taking into consideration that traffic always increases, if the bandwidth investment is large, it covers a long planning period while if it is small, it covers a small one. The distribution of this bandwidth to the VPs at the time of its installation is of less importance, because, afterwards, we can reallocate it dynamically, according to the actual offered traffic load which is determined for each service-class from the measured CBPs and the current bandwidth of each VP. The bandwidth reallocation procedure is executed so as to minimize the worst (maximum) CBP of all VPs of the network. That is, a global network optimization is carried out. In order to achieve this optimization, i.e. to improve the grade-ofservice of some badly sized VPs, eventually, the grade-of-service of some other VPs will deteriorate. The CBP of the service-classes accommodated to a VP expresses the grade-of-service, GOS, of this VP. For the purposes of network planning the bandwidth reallocation procedure is restricted, by deteriorating the CBP of those VPs which already have a less or equal GOS than the target GOS of the network, up to this target GOS (e.g. CBP=1%). After that, the bandwidth reallocation takes place only among the other VPs. To define analytically the network-planning optimization problem the same notations as in section 4.3 must be used. Then, the same mathematical programming model as the model for optimal VPB allocation can be formulated, but one more constraint-set must be added to express the specific demand of network planning. So, in the model of section 4.3 the following constraintset must be added: Due to demand for network-planning: for those VPs which meet a grade-of-service greater than, or equal to, target GOS, * V p = G ( GOS, A p )
*
where G stands for the function of calculating bandwidth from the offered traffic (Ap and a given grade-of-service, GOS). Likewise, the solution of this model is similar to the solution of the optimal VPB allocation problem, described in section 4.4. Again, the key point for its solution is to transform the nonlinear optimization model to a succession of linear integer programming models. Step 1 Define the target quality of service GOS of the network. For better understanding, suppose that the different service-classes will meet the same GOS in the Call Level. Calculate the initial worst and minimum CBP of the network xmax and xmin respectively, using the function G and based on the initial bandwidth allocation and the given traffic demand matrix. Step 2 Define a new improved worst CBP as:
xnew=(xmax+xmin)/2
Step 3 Find out whether the value xnew can stand for the worst CBP among all VPs or not, in the following way: (a) For those VPs which currently meet a grade-of-service greater than the * GOS: Calculate through G the Vp, based on Ap and using as grade-of-service the
19
xnew. (b) For those VPs which currently meet a grade-of-service lesser than or equal to the GOS: * Calculate through G the Vp, based on Ap and using as grade-of-service the GOS. Distribute all Vp’s to the VPs (i.e. define Wr) under the constraints posed by the installed bandwidth to the transmission links and according to the reliability scheme. The “primal cutting-plane algorithm” optimally achieves this distribution (see Appendix). Step 4 If the integer programming model has a feasible solution it means that all Vp’s are successfully distributed to the VPs and xnew can stand for the new worst CBP; in this case put xmax = xnew. Otherwise put xmin = xnew. Step 5 Repeat this procedure from Step 2 until the difference xmax-xmin becomes equal or less than an error value e, which expresses the accuracy by which the network's worst CBPs is estimated. Concisely, this procedure is presented in the flow-chart of Fig. 8. The proposed, herein, solution is analytical and optimal. An alternative solution can be achieved by the heuristic algorithm presented in reference [10], if this is modified so as to satisfy the constraint set C. The resultant solution will be sub-optimal as far as the worst CBP is concerned, however, it will satisfy well the immediate goal of network planning which is a maximum number of VPs to be produced with the target quality of service of the network.
6.
Application Examples of optimal VPB control
Two application examples are considered. The first example is for tutorial purposes. The second example presents the efficiency of the optimal VPB Control on the performance of a realistic ATM network.
6.1
Tutorial Example
The optimal VPB control is applied on the 3-node network of figure 2. For simplicity, the network accommodates one service-class which is the telephone service and it has been designed (dimensioned) so as to satisfy the Call-level QOS of 1% (CBP) for all switching (node) pairs. The designed traffic-load is 37 ERL for each switching pair per traffic-flow direction. The required number of trunks per VP is 49 (VP capacity); it results through the Erlang B-Formula. In practice, however, the trunks are provided in bundles (groups). As an example, if a bundle of trunks consists of 5 trunks, the VP capacity becomes 50 trunks. So, initially, the CBP for all switching pairs is 0.73% (
