Models for Network Design, Servicing and Monitoring of ... - CiteSeerX

Models for Network Design, Servicing and Monitoring of ATM Networks based on the Virtual Path Concept D. Medhi

Computer Science Telecommunications Program University of Missouri-Kansas City 5100 Rockhill Road Kansas City, MO 64110 USA Tel: +1 816 235-2006 E-mail: [email protected] FAX: +1 816 235-5159 Revised: April 1994, August 1994, February 1995 Initial version: December 1991

Abstract Virtual Path (VP) concept is gaining recently attention in terms of eective deployment of ATM networks. In this paper, we present models and algorithms for network design and management of ATM networks based on virtual path concept from a network planning perspective. Our approach is based on statistical multiplexing of trac within a trac class by using a virtual path for the class and deterministic multiplexing of dierent virtual paths, and on providing dynamic bandwidth and recon gurability through virtual path concept depending on trac load during the course of the day. For some realistic example networks, we observe that considering network dynamism through variation of trac during the course of a day by doing dynamic bandwidth and virtual path recon guration can save between 10 to 14 % in network design costs compared to a static network based on maximum busy hour trac.

Keywords: Wide-Area ATM Networks; Network planning, servicing and monitoring; optimization models; uid- ow approximation.

24 pages (including gures)

1. Introduction Broadband networks will support a variety of services such as voice, video, data, and image in an integrated environment. Asynchronous Transfer Mode (ATM) is considered the preferred transfer mode to support various services on broadband networks. These services are expected to have dierent trac characteristics, dierent qualities of service, and dierent bandwidth requirements and holding times. In an ATM Network, trac can be considered at the Virtual Path (VP) level, the call level, the burst level and the cell level [14]. Discussion on control issues at dierent levels can be found, for example, in [19], [25]. A connection-oriented transport mechanism is to be used for ATM networks. This means a virtual connection is required to be set up between the origin and the destination for a connection request. The call then uses this connection. There are two operational steps: in the call setup part, network resources are checked before the connection is allowed. Once the call is accepted, network trac management monitors the trac status and performs a policing function to ensure that resources are properly used and, accordingly, controls can be applied at dierent levels to satisfy quality of service. Recent volumes of periodicals have been devoted to various issues related to congestion control, protocol and switching for high speed networks, for example, see [20], [21], [22], [23]. Statistical multiplexing is possible at all levels of ATM-based networks. There are dierent implications due to introduction (or non-introduction) of multiplexing at dierent levels. For example, consider a network that does not use any virtual path connection (VPC); then all the trac can be statistically multiplexed on virtual channel connections (VCC) sharing common network links. Though this may result in minimum capacity networks, the VCC call establishment cost could be signi cant. This is because each VCC would need to negotiate a connection request at each intermediate node between source and destination [11]. On the other hand, if peak rates are allocated at each level, then resources would be poorly utilized. Thus, techniques are needed to make better use of available resources while providing probabilistic guarantees of quality-of-service (QoS). Use of virtual path as an eective transport technique and for resource management for ATM networks is gaining considerable attention recently [1], [10], [11], [12], [26], [27], [30], [38]. By grouping virtual circuits into a virtual path, an ATM-based network can be better managed. This can result in reduction of call set up time if there exists a virtual path (with enough capacity) between an origin and a destination since there is no need for extra processing at the intermediate 2

nodes. This will also allow calls of similar trac characteristics to be statistically multiplexed between an origin-destination pair. For ease of network management and control, virtual paths may be de ned for dissimilar trac types and can be deterministically multiplexed. This deterministic multiplexing of dierent virtual paths is likely to result in requirements of more network capacity than if everything is statistically multiplexed. However, at the same time, dynamic bandwidth control and virtual path rearrangement can be provided using VP concept. Thus, our approach considers statistical multiplexing of similar trac within a virtual path and deterministic multiplexing of various virtual paths along with dynamic bandwidth control and virtual path recon guration. (It should be noted that there are other works which have considered statistical multiplexing of heterogeneous trac streams, for example see [42], and the references in [19] and [35].) In this paper, we introduce a framework for network design and management for an ATMbased backbone network based on the virtual path concept. In this framework, we present models under the assumption that statistical multiplexing is applied to calls of similar trac and quality of service (QoS) characteristics over virtual circuits within a virtual path; but with deterministic multiplexing between dierent virtual paths for dierent services. The models are provided in an ATM trac network planning framework, i.e., models are presented for network design, servicing and monitoring. We address network dynamism in our models through dynamic bandwidth and virtual path recon guration based on trac requirements at dierent times during a day. Through computational results, we show that this dynamism can save a considerable amount in network design costs compared to static (during the day) virtual path based networks (details on network design algorithms can be found in [32]). It is worth mentioning that in recent years there have been some works in the literature that have addressed design of ATM Networks (e.g., [15], [29], [37]); however, these approaches are dierent than the approach we present here. The rest of the paper is organized as follows: in the next section, we start with a discussion of the role of virtual paths in ATM network and their bene ts; the issue of statistical multiplexing and deterministic multiplexing; and how they can be used in ATM network design. In section 3, we discuss issues during networking servicing and present models. Section 4 covers models for network monitoring for real time network-level ow control. In section 5, we present computational results on the cost of network design for dynamic bandwidth and virtual path recon gurable networks as compared to static (during the day) VP based networks.

3

2. Network Design Use of virtual path as an eective transport technique for ATM-based networks has been gaining considerable attention [1], [26], [38] (For discussion on role of VP in design and resource management, refer to [2], [4], [10], [11], [12], [13], [19], [27], [30]). A virtual path provides a logical direct link between virtual path terminators. Using virtual paths, an ATM network can be better managed by grouping virtual circuits into bundles [38]. Using VPs, exibility in trac management is possible due to separation of the logical transport network from the physical transmission network. For our work here, we assume that VCs of similar trac characteristics and Quality of Service (QoS) requirements are statistically multiplexed on a virtual path. For brevity, we will refer to it as STQoS types or classes. Note that more than one STQoS type may be preferable between an origin-destination pair for trac of signi cantly dierent trac characteristics and requirements. For example, it may be preferable to have an STQoS type de ned for real-time services and another for non-real time services. Use of VP simpli es B-ISDN call processing and reduces call establishment time since there is no processing required at the intermediate nodes. For example, as presented in [38], the explicit scheme can be used in the cell header organization of virtual paths. This way, processing on a call-by-call basis at each intermediate node can be eliminated during call establishment and release; consequently, call set up time can be signi cantly reduced. Alternately, the network can be a collection of ATM switches and ATM cross-connect systems where the trac demand between two end ATM switching nodes can be cross-connected at intermediate points using ATM cross-connect systems [12], [30]. There are also other advantages in using virtual path concept as noted in [19]: class of service control is easier to implement than when dierent types of trac are supported over the same virtual path; dynamic bandwidth control is easier to implement per path due to similar trac characteristics; multiplexing several classes of trac, with dierent characteristics, decreases the multiplexing gain compared to the multiplexing of trac with same characteristics [33], [34]. Based on the above advantages of the VP concept, we assume the following for eective network design and management: we allow statistical multiplexing between calls of the same STQoS class over virtual circuits within the virtual path allocated for this STQoS type; however, we assume no statistical multiplexing between dierent virtual paths for dierent STQoS classes (i.e., only deterministic multiplexing). As mentioned before, a key advantage is that call processing time can be signi cantly reduced due to the introduction of VPs. In addition to the bene ts that are already discussed, we note the following: each virtual path for each STQoS type is assigned a certain 4

bandwidth which determines the number of virtual channels it can support to provide satisfactory QoS. Following [10], we consider that when bandwidth is reserved on a VP, a limit is placed on the number of calls and bursts in progress on that VP at any time. This also simpli es the control decision to verify the number of calls and bursts in progress compared to allocated maximum. Further, the use of the concept of statistical multiplexing among VCs of same STQoS type in a VP and deterministic multiplexing of dierent VPs simpli es the non-linear optimization problem of network dimensioning so as to meet certain QoS guarantees for given trac demand. Speci cally, it has the following major advantage: it decouples the problem of determining the bandwidth needed on each virtual path for each STQoS type and the associated problem of determination of virtual paths for each STQoS type and sizing of the network. The work here is based on this key advantage of decoupling of the bandwidth estimation problem and the VP routing and network sizing problem. We rst discuss the second problem, i.e., our model for the VP routing and network sizing problem. In the framework of a network, there are a number of possible virtual paths that an STQoS type can take between two switching end points (or a demand pair). There are possible demands between any two ATM switching nodes in the network (demand pairs). Thus, we consider the determination of virtual path for each STQoS type and each demand pair in the network. Given the estimated bandwidth required for a particular STQoS type and between two ATM switching end points, we then need to determine one of the paths (non-bifurcated routing) from the list of the possible (candidate) virtual paths between the end points that use ATM cross-connect nodes at intermediate points (for setting up a VP). Note that a virtual path is constructed by connecting one or more network links. Additionally, for a particular demand pair, dierent virtual paths may be taken by dierent STQoS types. For example, consider Fig. 1. Here for the demand pair A-D, STQoS type s = 1 takes the route A-B -D, while STQoS type s = 2 takes the route A-C -B -D. Due to the ow of trac on dierent virtual paths, we can determine the total trac on each link of the network by adding for dierent pairs and dierent STQoS types that use this link (this is due to deterministic multiplexing of dierent STQoS types). For the formulation we are about to present for the VP routing and network sizing problem, we assume that we are given a set of possible links for which capacity has to be determined (network sizing). To mathematically represent the problem, we introduce the following notations:

K The set of node (demand) pairs in the network S The set of STQoS types for pair k 2 K k

5

L The set of links in the network P The set of possible candidate virtual paths for STQoS type s 2 S , demand pair k 2 K x Virtual path routing variables { 1 if STQoS type s 2 S , k 2 K uses path j 2 P ; 0 s k

k

s kj

s k

k

otherwise

b Estimated bandwidth requirement for STQoS type s 2 S , k 2 K s k



s` kj

k

Link-path incidence matrix; 1 if path j 2 P for STQoS s 2 S and for pair k 2 K uses link ` 2 L; 0 otherwise s k

k

y Sizing (topology) variables; the number of units of high capacity on link ` 2 L `

 Capacity of a high capacity unit on a link C Cost of a high capacity unit on link ` 2 L `

The network dimensioning problem can be formulated as follows: min

X

f g 2L x;y

subject to

X s j 2P k

Cy `

(1a)

`

`

x = 1; s 2 S ; k 2 K s kj

X X X

k

(1b)

 b x  y ; ` 2 L

(1c)

x = 0 or 1; j 2 P ; s 2 S ; k 2 K

(1d)

y  0 and integer; ` 2 L

(1e)

k

2K 2Sk 2Pks s

s` kj

s k

s kj

`

j

s k

s kj

`

k

In the above network dimensioning model (1), the objective function (1a) represents the total capacity cost on links. (1b) and (1d) are the decisions of choosing a virtual path for a STQoS type for a node pair. Constraint set (1c) ensures that the bandwidth required on each link due to trac

ow for dierent STQoS types and demand pairs is satis ed by the appropriately determined link capacity. Note that, in this formulation, dierent node pairs are allowed to have dierent number of STQoS classes. This is bene cial when a new STQoS is introduced for some demand pairs due to community of interest, and not for others. This model takes possible candidate paths as an input; these candidate paths, for example, can be generated using a k-shortest path algorithm [28]. Further, the idea of candidate paths is advantageous in restricting (or allowing) choice of certain 6

paths due to information available from various network elements based on network growth and thereby, preprocessing the set of candidate virtual paths (hence the link-path formulation). In the above model (1), we assume that the bandwidth estimate b for STQoS s 2 S , k 2 K is available. We now discuss how the quantity b can be estimated. For trac types given with three trac descriptors (utilization, mean burst period, peak rate), Anick et al [3] have proposed a method for computing buer over ow probability for two-state, on-o trac to a link based on the uid- ow approach. (It is worth noting that Guerin et al [18] have presented an equivalent bandwidth estimation method based on the approach [3] for computation in real-time. Also, capacity design for a single entity (link or path) based on a quality of service requirement speci ed by p-th percentile delay of m cells has been presented by Sato and Sato [39]). We adapt here the

uid- ow approach to estimate b for each STQoS type s 2 S , pair k 2 K. A brief description of this process is included in Appendix. For convenience, we refer to it as InvAMS procedure. We note here that if each connection for a particular STQoS type requires peak rate allocation, e.g., class-1 trac in BISDN [9, p. 135], then for trac requirements given in oered load (erlangs) and for a quality-of-service given in terms of blocking probability, the inverse Erlang-blocking formula can be used [24] to determine capacity required. Thus, in the case of class-1 trac, there is no statistical multiplexing of connections within an STQoS type. For the rest of the discussion and clarity, we will refer only to InvAMS procedure and consider statistical multiplexing of trac within an STQoS class. s k

k

s k

s k

k

We have discussed the decoupled network design problem of estimating b and solving the VP routing and link sizing problem. To summarize, we have the following algorithm to solve the network design problem. s k

Algorithm-A Step 1 For given QoS for dierent STQoS types and node pairs, compute b using InvAMS procedure for s 2 S , k 2 K. s k

k

Step 2 Generate candidate set of virtual paths P for s 2 S , k 2 K. s k

k

Step 3 Size network by solving model (1). The network design models mentioned above can be used for ATM trac network planning, similar to the planned servicing phase [7] for dynamic non-hierarchical routing circuit-switched 7

networks [5]. This type of planning cycle is typically one to two years [7]. The models can be used primarily for network sizing. We now discuss a better model than model-(1) that incorporates the variation in trac from one hour to another during the day (multi-hour model). This is desirable as this results in a more ecient network design (see the section on results) than using (1) with maximum busy hour trac over all the hours during a day. Of course, multi-hour approach means estimating b for dierent hours of the day. This provides us with dynamic virtual path bandwidth control and dynamic VP based recon gurabilty for better use of resources. On the other hand, model (1) represents the design problem considering only maximum busy hour trac for each pair and STQoS type. We now present an extension of model (1) incorporating time of the day (hour to hour) variation. (It should be noted that multi-hour design for dynamic call routing circuitswitched networks has resulted in considerable network savings compared to maximum busy hour network design [5].) Our work here considers dynamic bandwidth control with dynamic network recon gurability based on virtual path for ATM-based broadband networks. (In the context of circuit-switched networks, dynamically recon gurable networks have been addressed in [6], [8], [16], [17].) Towards this end, we assume that the day has been clustered into several load periods (H) and we introduce a superscript h 2 H to represent dierent load periods. Note that H need not be all the hours of a day; it can be clustered into important trac load change periods during a day. K, S , L are as described above. The new notations, incorporating h, are described below: s k

k

P

sh k

x

sh kj

The set of possible candidate virtual paths for STQoS type s 2 S , demand pair k 2 K used for all h 2 H k

Virtual path routing variables { 1 if STQoS type s 2 S , k 2 K uses path j 2 P in h 2 H; 0 otherwise sh k

k

b

Estimated bandwidth requirement for STQoS s 2 S , k 2 K, h 2 H



Link-path incidence matrix; 1 if path j 2 P for STQoS s 2 S and for pair k 2 K in h 2 H uses link ` 2 L; 0 otherwise

sh k

s`h kj

k

sh k

k

y Sizing (topology) variables; the number of units of high capacity on trac link ` 2 L `

 Capacity of a high capacity unit C Cost of a high capacity unit on link ` 2 L `

8

The following model can be used for multi-hour design of a dynamically recon gurable VP routing network: X min Cy (2a) f g x;y

subject to

X j

2Pksh

2L

`

`

`

x = 1; s 2 S ; k 2 K; h 2 H sh kj

k

X X X k 2K s2Sk j 2P sh k

 b x  y ; ` 2 L; h 2 H s`h kj

sh k

sh kj

`

(2b) (2c)

x = 0 or 1; j 2 P ; s 2 S ; k 2 K; h 2 H

(2d)

y  0 and integer; ` 2 L

(2e)

sh kj

sh k

k

`

Here the path chosen for each service at dierent time of the day may be dierent ((2b)). Constraints (2c) say that the link ow at each load period is going to force the determination of capacity on the link. [Note also that although we have assigned a dierent set of candidate paths for each load period and service for each trac pair, this need not be dierent; however, explicit notation here allows us the exibility in the case the candidate set of paths are dierent.] Now the above multi-hour model can be used in determining link size for given trac requirements and QoS: Algorithm-B Step 1 For given QoS for dierent STQoS types and node pairs and for dierent load periods, compute b using InvAMS procedure for s 2 S , k 2 K; h 2 H. sh k

k

Step 2 Generate candidate set of virtual paths P for s 2 S , k 2 K; h 2 H. sh k

k

Step 3 Size network by solving multi-hour model (2). The model (2) assumes that there is no capacity that exists in the network. In most real networks, the network sizing needs to determine additional capacity needed in the next planning period to satisfy trac demand based on the existing link capacity in the present planning period. This can be easily modeled by changing one constraint, (2c), from model (2) to X X X k

2K 2Sk 2Pksh s

 b x   + y ; ` 2 L; h 2 H s`h kj

sh k

sh kj

`

j

9

`

(2c0 )

where now y stands for additional capacity units (instead of total units) required on link ` 2 L, and  represents existing capacity on link `; and the rest of the model remains the same. For ease of reference, we call this model (20 ). Note that a similar model for maximum busy hour case can also be written. `

`

3. Network Servicing We discussed in the previous section the network design aspect of an ATM backbone network. Once the network is sized based on forecasted load, the capacity of the network, i.e., fy g from model (1), or, f  + y g from model (2), ` 2 L are known. If there is no error in forecasted load, the network design method discussed in the previous section is sucient to satisfy the load; no correction is needed. However, load uncertainties occur due to various sources of errors [7], thereby requiring the need for network servicing in a shorter cycle time (less than a week to a few weeks) than the typical cycle time of the network design phase. For the purpose of this discussion, network service is similar to demand servicing for dynamic nonhierarchical routing circuit-switched network, as discussed in [7]. During the network servicing process, the capacity of the links usually remains the same (not virtual path bandwidth) as the topological variables are known from the network design phase as discussed earlier. However, in the network servicing phase, we have more recent information about the load for dierent STQoS types from collection of trac data. Thus, reserved bandwidth for dierent STQoS types would change and, thereby, virtual path routing would possibly change. Additionally, for broadband networks new STQoS classes may need to be introduced that were not anticipated during the network design phase. This might happen from two sources: analysis of recent trac data resulting in a new STQoS class that can not be classi ed in any of the previous STQoS classes de ned and actual introduction of a new service class. Thus, new STQoS classes, not anticipated during the network design phase, may be introduced. This can be accomplished in our framework through updating of the set S . For any new STQoS type, again, the InvAMS procedure can be used to estimate the bandwidth required. Also, based on any anticipated network congestion, the set of virtual paths P can be updated. Normally, the problem we solve in the network servicing phase is updating the bandwidth required for various STQoS classes and the determination of virtual path routing based on the updated information so as to maximize revenue or throughput while providing an acceptable QoS. The additional notations used here are: `

`

`

k

s k

Capacity of link ` 2 L obtained from network design phase `

10

w Revenue per unit of bandwidth for s 2 S , k 2 K. s k

k

^b Minimum acceptable amount of bandwidth to be carried for s 2 S , k 2 K. s k

k

z ow amount on path j for pair k and service s (this is set to zero if the path j is not s kj

selected; see the discussion below)

To summarize, the following quantities are updated: S , P , w , b . Particularly, if a new STQoS class is anticipated, this can be included through updating the set of STQoS classes S , and the associated bandwidth estimate b (and ^b ). The following is a mathematical formulation of the virtual path routing problem to maximize revenue for the network servicing phase: k

s k

s kj

s k

k

s k

max f g x;z

subject to

X j 2P s k

s k

X X k

2K 2Sk

w

s

s k

X j 2P s k

z

s kj

x = 1; s 2 S ; k 2 K s kj

k

(3a) (3b)

z x b ; j2P ; s2S ; k2K

(3c)

X

z  ^b ; j 2 P ; s 2 S ; k 2 K

(3d)

X X X

(3e)

s kj

s kj

j 2P s k

s kj

s k

s k

k

s k

s k

k 2K s2Sk j 2P s k

k

 z  ; `2L s kj

s` kj

`

x = 0 or 1; j 2 P ; s 2 S ; k 2 K

(3f )

z  0; j 2 P ; s 2 S ; k 2 K

(3g )

s kj

s k

s kj

s k

k

k

Explanations of above expressions are similar to model (1) and (2); the rst dierence is in objective function due to the knowledge on network size from the network design phase; the objective function (3a) is now the maximization of total revenue. The additional variables, fz g, is for ow on path j for trac pair k for STQoS class s. (3b) means the same as in (1b). (3c) speci es that the bandwidth ow amount z , on a path if chosen should not be more than the required ow; otherwise, force the ow to be zero for the paths not chosen. The constraint set (3d) requires that the total ow should be more than a minimum amount (to satisfy a pairwise minimum QoS requirement for each service). (3e) is the bound on link ow for all dierent trac streams that use the link. Though, normally, problem (3) is expected to be feasible, it may so happen that due to introduction of new STQoS types and trac uctuation or updated trac s kj

s kj

11

information, the updated b produced by InvAMS procedure resulting in change in the minimum requirement ^b can make the problem (3) infeasible. In this case, to provide satisfactory QoS, capacity augmentation on some (all) of the link would be needed. This can be accomplished, when and if needed, by solving the incremental model (20 ) discussed at the end of the previous section; this shows another use of model (20 ). Notice that in model (3) the superscript h for dierent load periods during the day is omitted since the revenue optimization problem (2) can be solved separately for each load period to generate dierent optimal routes for dierent load periods; at the same time, this provides dynamic recon gurability of VPs. Further, we note here that use of the following objective X X X z (3a0 ) max s k

s k

f g x;z

k 2K s2Sk j 2P s k

s kj

results in maximization of throughput, instead of revenue. To summarize, the algorithmic steps in the network servicing phase can be the following: Algorithm-C Step 1 Update S (k 2 K), if needed. k

Step 2 For given QoS for dierent STQoS types and node pairs, compute b using InvAMS procedure for s 2 S , k 2 K for each trac load periods based on updated trac information. s k

k

Step 3 Generate updated candidate set of virtual paths P for s 2 S , k 2 K. s k

k

Step 4 Solve optimal virtual path routing model (3) for each trac load period. If (3) is feasible, then stop, else go to step 5. Step 5 Solve incremental augmentation model (20 ). Given the present trend in price reduction of computer memory and hardware, the optimal virtual paths generated in this phase can be stored for table look up in (near) real-time for time epochs when load during the day changes.

12

4. Network Monitoring Usually, the bandwidth estimate and the con guration map obtained from the network servicing phase can be used for real-time deployment in the network. However, network overload, load uctuation and outages do occur. Thus, real time network monitoring and control is needed to address such problems. To respond to these situations, the advantages from use of VPs due to separation of the logical transport network from the physical transmission network can be fully utilized [19]. The added exibility is that the virtual path capacity can be changed without the need to change the physical interface. Thus, adaptive bandwidth control and virtual path rearrangement are possible. These exibilities can be capitalized in real time network monitoring through a network-level ow control to provide satisfactory performance guarantee. Note that we have assumed that by reservation of bandwidth per VP, a limit is placed on the number of calls and bursts in progress on that VP and our discussion here is primarily limited to network-level issues. (For a discussion on other call level controls and on cell level controls, and on bandwidth allocation, refer to [19], [35] [43] and the references therein). As stated earlier, from network servicing, we have an estimate on the number of connection attempts at dierent times during the day; this can be used (based on acceptable grade-of-service) to determine the limit on the number of calls of each service time at dierent times during the day. For minimum, this limit can be provided for each hour of the day (for each service and trac pair). A limit on the number of calls allowed also provides a limit on the total bandwidth allowed for the accepted calls (based on InvAMS). If the demand on the bandwidth is found to be more than the allowed maximum bandwidth for this STQoS class, then cell- and burst-level policing function should limit the amount of cells admitted to the network for that trac class for the accepted calls so as to maintain quality-of-service (see, for example, Onvural [35] for further discussion and other references). If however, at the network-level, the call blocking probability is found to be signi cantly higher than the acceptable grade-of-service, a new estimate on how many calls should be admitted for this STQoS class and for the speci c pair be computed. (To compute such an estimate, call attempt statistics may be collected every ve minutes.) Based on this new estimate on the limit on calls, new bandwidth estimate is required, and, if needed, a virtual path rearrangement is required. However, this is required only for these subset of STQoS classes (which did not satisfy grade-of-service requirement) and only for some of the demand pairs. Thus we need to consider, a subset of STQoS classes S  S , K  K. Also, a restricted set of candidate paths, k

k

13

P  P , may be used. The following model can then be used for the virtual path routing for the s k

s k

subset of STQoS classes.

X X

max

f g x;z

subject to

X s j 2P k

2

k

2

K s

S

w

s k

k

X j

2

P

s k

z

(4a)

s kj

x = 1; s 2 S ; k 2 K s kj

(4b)

k

z x b ; j2P ; s2S ; k2K

(4c)

X

z  ^b ; j 2 P ; s 2 S ; k 2 K

(4d)

X X X

(4e)

s kj

s kj

s j 2P k

s kj

k

2

s k

s k

s k

s k

2

K s

S

k

k

j

2

P

s k

k

 z  ; `2L s` kj

s kj

`

x = 0 or 1; j 2 P ; s 2 S ; k 2 K

(4f )

z  0; j 2 P ; s 2 S ; k 2 K

(4g )

s k

s kj

s kj

s k

k

k

Note that in model (4), is the unused capacity that is presently available on link ` in addition to the capacity that is presently assigned to the aected STQoS groups that uses this link (since this will be released for virtual path rearrangement). Thus, routing and rearrangement are done on the basis of what is available in the network. Note also that the size of the problem (4) is smaller than (3) as the model is needed to be solved on a subset of STQoS classes and pairs. The following dynamic bandwidth estimation and virtual path routing/rearrangement algorithm may be used for network monitoring at network-level ow control: `

Algorithm-D Step 1 Based on call attempts during a time window, determine subsets S  S , K  K that need correction. k

k

Step 2 For given QoS for dierent STQoS types and node pairs, compute new b using InvAMS procedure for s 2 S , k 2 K based on collection of trac. s k

k

Step 3 Generate updated candidate set of virtual paths P for s 2 S , k 2 K and associated cost w . s k

k

s kj

Step 4 Solve virtual path routing model (5) to generate rearrangements. 14

A possible way to implement the above algorithm is to measure call attempt statistics at each node every ve minutes (time window) and to communicate these measurements to a central VP processor [11]. Due to real-time nature, a heuristic approach to solve model (4) can be taken. In this case, after the computation of VP bandwidth and VP routing/rearrangement, the results, if any, will be communicated back to the nodes.

5. Numerical Results In this section, we present results for network dimensioning models discussed in section 2 and show the impact of using a multi-hour model as opposed to single hour model using maximum busy hour trac. For this computational result, we have used only one trac type in each STQoS class. It should be noted that although theoretically, each possibly conceivable trac type can be an STQoS class by itself, in practice this would generate too many classes and could become an administrative nightmare for network operations and management. How to classify various trac types under a single STQoS class or group into dierent STQoS classes is itself a complex problem. For example, Suruagy Monteiro [41] has addressed this problem in terms of whether to integrate or not (see also [42]) | this issue certainly deserves further investigation. For the purpose of our numerical results, we consider here two STQoS classes. To obtain the results, we use three realistic example networks which we have used in other studies [31]; these example networks are extracted from an actual voice network spanning the continental US. Topological information for these example networks are given in Table 1 (also see Figures 2, 3 and 4). [Note that in these networks a circle and a square together means that an ATM switching node is co-located (same city) with an ATM cross-connect node.] The average number of sources to be connected for the voice trac for these networks for three dierent times during a day (morning, early afternoon and late afternoon) i.e, #(H) = 3, are considered. [For brevity, we refer to these three load periods as ld-1, ld-2, and ld-3, respectively.] Since at this point we do not have realistic trac data available to us for any emerging trac, we used a ctitious trac for the second STQoS type. The average number of sources of this STQoS class for dierent trac pairs in the network for various time of the day are generated using a uniform random number generator by picking a number between 0 and 20 % of the number of sources for the voice trac   (i.e, N 2 = Uniform (0; 1)  0:2N 1 , where N is the average number of trac sources to be connected for service s, trac pair k in load period h, and where dxe returns the smallest integer higher than x). The total trac in terms of number of sources for dierent times of the day and h

k

h

k

sh k

15

busy hour are listed in Table 2. (It should be noted that the total trac in a particular load hour being bigger than other load hours does not mean this relation holds for each individual trac pair.) For the voice trac, following [40], we have used the following parameters for trac descriptors for packetized voice procedure: utilization () = 0.6487, mean burst period (m) = 352 ms, peak rate (Rpeak ) = 32 Kbps (for ADPCM coding); these values are used in computing bandwidth requirement using InvAMS procedure for buer over ow probability, p, of 10?4 .The parameters used for the second type are:  = 0:2, m = 300 ms, Rpeak = 300 Kbps; the buer over ow probability used is 10?7 . The trac descriptors and the QoS requirements are summarized in Table 3. Note the dierence between these two trac types: the second trac has a peak rate which is an order of magnitude more than the voice trac, has lower utilization and mean burst period, while the over ow probability is much more stringent for the second trac type. We assume that separate buer for each trac type is provided and is assumed to be 1 Mb each (this is used by InvAMS procedure to estimate bandwidth). Network

No. of ATM Switches

EN-1 EN-2 EN-3

7 10 15

Table 1:

Table 2:

No. of Trac Pairs, #(K) 21 45 105

No. of ATM Cross- No. of -Connect Nodes Links, #(L) 10 18 23

14 27 33

Network Topology information for example networks

Network

ld-1 s=1/s=2

ld-2 s=1/s=2

ld-3 s=1/s=2

Busy Hour s=1/s=2

EN-1 EN-2 EN-3

1652/168 2687/263 4687/488

1091/139 2830/321 4082/395

1530/189 3226/349 4956/491

1661/247 3531/473 5442/691

Summary of Network Trac (in terms of total number of sources) for example networks

16

Services



m

Rpeak

s=1 s=2

0.6487 0.2

352 ms 300 ms

32 Kbps 300 Kbps

Table 3:

Buer over ow probability, p 10?4 10?7

Trac Descriptors and QoSs for two services

Given the average number of sources (and the parameters listed in Table 3), InvAMS procedure is used to compute the bandwidth requirements, i.e.,

b = InvAMS (N ; (Rpeak ) ;  ; m ; r; p ); s 2 S ; h 2 H; k 2 K: sh k

sh k

s

s

s

s

k

Model (2) is an integer programming problem and is suspected to be NP-complete [36]. If M denotes the number of nodes, then #(K) = M (M ? 1)=2 (here, # denotes the cardinality of a set). If we assume that the number of paths variables for each s, h and k to be P , then the total number of constraints is LH + SHM (M ? 1)=2 and the number of integer variables is SHPM (M ? 1)=2+ L (where L = #(L); H = #(H); S = #(S )). Typically, L is in the order of M for a ber-optic based transmission network. If we assume the number of candidate paths to be in the order of M , then we can see that for xed H and S , as the number of nodes grows, the number of constraints grows by M 2 and the number of variables by M 3 . In a companion paper [32], we have presented details on a decomposition algorithm for model (2) based on duality and subgradient optimization by exploiting the structure of the problem. The candidate paths are generated using a k-shortest path algorithm [28]. We have used the modular grouping value, , for capacity unit of a link to be 1.5 Mbps (  T1 rate). Given the trend that the ber cost is comparatively low compared to port cost at the nodes, we have computed unit cost of link of 1.5 Mbps using 100 as the cost of each termination port and 0.1 to be the distance cost per mile. Thus, C = 2  100 + 0:1  D , where D is the distance in mile for link ` per 1.5 Mbps unit link. `

`

`

In Table 4, we report the cost of the three networks using single maximum busy-hour and multi-hour design (Algorithm-A and Algorithm-B, respectively). Observe that the multi-hour design approach with dynamic bandwidth and virtual path recon gurability saves between 10 and 17

14 % in cost compared to maximum busy-hour design while providing the same quality of service. As has been done for dynamic call routing circuit-switched networks [5], we have now shown that multi-hour approach for dynamically recon gurable broadband networks can provide cost savings compared to static (during the day) network design. Our implementation in C language, for solving Algorithm-B, on a DEC Alpha AXP running OSF/1 operating system (Model 3000/400, 64MB main memory, SPECfp 92 benchmark = 112.5) took about 4 seconds for EN-1, 27 seconds for EN-2, 127 seconds for EN-3; thus, a good solution can be found in a reasonable amount of time. Network

Busy Hour Design

Multi-Hour Design

Savings

EN-1 EN-2 EN-3

15,278.90 57,129.90 91,098.90

13,402.00 51,485.10 81,599.10

14.00 % 10.96 % 11.64 %

Table 4:

Cost of Network Design

6. Discussion In this paper, we have presented models for network design and management for an ATM backbone network. Problems are formulated for network design, servicing and monitoring. These are based on the virtual path concept. The VP concept provides an eective way to manage an ATM network. Various advantages of virtual path concept are noted in Section 2. For example, by allowing statistical multiplexing within the same STQoS type in a virtual path for a particular demand pair, the call set up time can be signi cantly reduced. Exploiting the versatility of VP concept and assuming that only deterministic multiplexing is allowed between dierent VPs, we have made the following contributions: we have identi ed that, due to statistical multiplexing of calls within STQoS type using VPs and deterministic multiplexing between VPs, the network design problem can be decoupled into bandwidth estimation problem and virtual path routing and network sizing problem; we have given a framework on trac network planning for ATM networks in terms of network design, servicing and monitoring; based on the observation on decoupling, we then provide mathematical models and algorithms that can be used in solving the speci c problems that arise in each phase of network design, servicing and monitoring; using multi-hour model, we 18

have considered a dynamic bandwidth control and dynamic virtual path recon gurable network; we identi ed how a new STQoS type can be introduced during network servicing phase; we observe the dynamic network rearrangement exibility during network monitoring through solution of a subset model to provide maximum network utilization; nally, through computational results, we show the cost saving between 10 to 14 % with multi-hour dynamic broadband network compared to static maximum busy-period based networks. It may be noted that in our approach, we have not explicitly taken into account delay requirements. As typical with uid- ow based approach used by others (see, for example, [3], [18], [42]), we have considered here only also the loss probability. Because of the architecture we are presenting in this paper, the delay constitutes the processing delay at the origination and destination swiching nodes and transmission delay on links (no processing delay at the intermediate cross-connect nodes). We believe the delay requirement for a particular service will probably force the selection of candidate paths and the number of links that can constitute a candidate path (to address delay due to transmission on links). Thus our arc-path approach is also suitable for this consideration. However, further work is necessary in this direction.

Appendix We present the InvAMS procedure here. For simplicity, consider one STQoS type and one demand pair. InvAMS procedure requires a subroutine to compute over ow probability based on the two-state, uid ow model with in nite buer due to Anick et al [3] ; henceforth, called the AMS procedure. (It may be noted that Suruagy Monteiro et al [42] have presented another approach based on Tucker's work [44] on uid- ow model with nite buer.) In AMS approach, each trac source is either in idle state (no transmission) or burst state (transmission at peak rate). We assume that the burst and idle period are i.i.d. and exponentially distributed, then a trac source can be characterized by the following three parameters:

 := utilization, fraction of time the source is active m := mean burst period Rpeak := Peak rate If 1= and 1= are mean idle and burst period, then  = m1 ;  = m(1? ) : 19

Consider N sources. If F (r) is the equilibrium probability that i sources are active and the buer length does not exceed r and F = 0 for i 2= [0; N ], then the set of dierential equations governing the equilibrium buer distribution can be given by [3] i

i

(iRpeak ? b) dFdr(r) = (N ? i + 1)F ?1 ? f(N ? i) + igF + (i + 1)F +1 ; i

i

i

i

i 2 [0; N ]

where b := capacity (bandwidth). In matrix notation:

D dxd F(r) = MF(r);

r  0:

The following eigen problem can be solved analytically [3]

zD = M (z is some eigen value of D?1 M, and  is the associated right eigenvector). The probability of over ow beyond r is given by

p = 1 ? 1 F(r) = ?

N

?b

b=Rpeak

T

X

=0

c?1

e i a (1  ): z r

i

T

i

i

(Here 1 is a vector of 1's.) Thus, given N , , m, Rpeak , b, and buer size, r, the over ow probability can be computed based on the above approach by [3]. For brevity, we denote this procedure as AMS (N; Rpeak ; ; m; b; r). T

To compute the bandwidth required for given N , , m, Rpeak , r and acceptable over ow probability p^ (QoS), a simple bisection scheme as given below can be used (this is what we refer to as InvAMS procedure): procedure InvAMS (N; Rpeak ; ; m; r; p^): Estimate b and b such that p = AMS (N; Rpeak ; ; m; b ; r) < p^ < AMS (N; Rpeak ; ; m; b ; r) while ( j log(p) ? log(^p) j >  ) do /* for some tolerance  > 0 */ b = (b + b )=2 p = AMS (N; Rpeak ; ; m; b; r) if ( p > p^ ) then b =b else b =b endif endwhile return(b) l

h

h

l

l

h

l

h

20

Acknowledgement The network data used in this work is based on data provided for another work [31] by Sprint Corporation and is greatly appreciated. We are thankful to the anonymous referees for many helpful comments and for bringing to our attention several references which certainly helped improve the content and the presentation of this paper.

References

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[16] G. Gopal, C. Kim and A. Weinrib, \Dynamic Network Con guration Management," Proceedings of IEEE International Conference on Communications (ICC'90) , pp. 295-301, 1990. [17] G. Gopal, C. Kim and A. Weinrib, \Algorithms for Recon gurable Networks," 13th International Teletrac Congress , Copenhagen, Denmark, pp. 341-347, June 1991. [18] R. Guerin, H. Ahmadi and M. Naghshineh, \Equivalent Capacity and its Application to Bandwidth Allocation in High-Speed Networks," IEEE J. on Selected Areas in Comm., Vol. 9, no. 7, pp. 968-981, 1991. [19] I. W. Habib and T. N. Saadawi, \Controlling Flow and Avoiding Congestion in Broadband Networks," IEEE Comm. Magazine , Vol. 29, No. 10, pp. 46-53, Oct 1991. [20] IEEE Communications Magazine, special issue: \B-ISDN: High Performance Transport," Vol. 29, No. 9, Sept 1991. [21] IEEE Communications Magazine, special issue: \Congestion Control in High Speed Networks," Vol. 29, No. 10, Oct 1991. [22] IEEE Journal on Selected Areas in Comm. Issue on \Congestion Control in High-Speed Packet Switched Networks," Vol. 9, No. 7, 1991. [23] IEEE Journal on Selected Areas in Comm. Issue on \Large-Scale ATM Switching Systems for B-ISDN," Vol. 9, No. 8, 1991. [24] D. L. Jagerman, \Methods in Trac Calculation," AT&T Bell Labs. Tech. Journal , Vol. 63, No. 7, pp. 1283-1310, 1984. [25] K. Kawashima and H. Saito, \Teletrac Issues in ATM Networks," Computer Networks & ISDN Systems , Vol. 20, pp. 369-375, 1990. [26] T. Kanada, K. Sato and T. Tsuboi, \An ATM based Transport Network Architecture," IEEE COMSOC Intl. Workshop on Future Prospects of Burst/Packetized Multimedia Comm., Osaka, Japan, pp. 2-2, Nov 1987. [27] R. Kawamura, K.-i. Sato and I. Tokizawa, \Self-Healing ATM Networks Based on Virtual Path Concept," IEEE J. Sel Areas in Comm., Vol. 12, pp. 120-127, 1994. [28] E. L. Lawler, Combinatorial Optimization: Networks and Matroids , Holt, Rinehart and Winston, New York, 1976. [29] K. Lindberger, \Dimensioning and Design Methods for Integrated ATM Networks," 14th International Teletrac Congress , Antibes, France, pp. 897-906, June 1994. [30] M. Logothetis and S. Shioda, \Centralized Virtual Path Bandwidth Allocation Scheme for ATM Network," IEICE Trans. Comm., Vol. E75-B, no. 10, pp. 1071-1080, 1992. [31] D. Medhi, \A Uni ed Approach to Network Survivability for Teletrac Networks: Models, Algorithms and Analysis," IEEE Trans. on Communications , Vol. 42, pp. 534-548, 1994. [32] D. Medhi, \Multi-Hour, Multi-Trac Class Network Design for VP-based Wide-Area Dynamically Recon gurable ATM Networks," Proceedings of IEEE INFOCOM'95 , Boston, MA, April 1995. [33] T. Murase, H. Suzuki and T. Takeuchi, \Continuous Bit Stream Oriented Services in ATM Networks," Proc. 2nd IEEE COMSOC Intl. MULTIMEDIA Workshop , April 1989. 22

[34] K. Noguchi, T. Okada and H. Ohnishi, \Resource Management in ATM Networks," Proc. 2nd IEEE COMSOC Intl. MULTIMEDIA Workshop , April 1989. [35] R. O. Onvural, Asynchronous Transfer Mode Networks: Performance Issues , Artech House, Boston, MA, 1994. [36] C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity , Prentice-Hall, Englewood Clis, NJ, 1982. [37] C. M. D. Pazos, J. A. Suruagy Monteiro and M. Gerla, \Topological Design of Multiservice ATM Networks," Proceedings of SBT/IEEE ITS'94 , Rio de Janeiro, Brazil, pp. 385-389, 1994. [38] K.-I. Sato, S. Ohta and I. Tokizawa, \Broad-Band ATM Network Architecture Based on Virtual Paths," IEEE Trans. on Communications , Vol. 38, pp. 1212-1222, 1990. [39] Y. Sato and K.-I. Sato, \Virtual Path and Link Capacity Design for ATM Networks," IEEE Journal on Selected Areas in Communications , Vol. 9, pp. 104-111, 1991. [40] K. Sriram and W. Whitt, \Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data," IEEE J on Selected Areas in Comm., Vol. SAC-4, No. 6, pp. 833-846, 1986. [41] J. A. Suruagy Monteiro, Bandwidth Allocation in Broadband Integrated Services Digital Networks , Ph.D. dissertation, Report No. CSD-900018, Computer Science Department, University of California-Los Angeles, CA, July 1990. [42] J. A. Suruagy Monteiro, M. Gerla and L. Fratta, \Statistical Multiplexing in ATM Networks," Performance Evaluation , Vol. 12, pp. 157-167, 1991. [43] J. A. Suruagy Monteiro and M. Gerla, \Bandwidth Allocation in ATM Networks," Annals of Operations Research , Vol. 49, pp. 25-50, 1994. [44] R. C. F. Tucker, \Accurate Method for Analysis of a Packet-Speech Multiplexer with Limited Delay," IEEE Trans. on Comm., Vol. 36, pp. 479-483, 1988.

B s=1

A

D Switching Node s=2

Cross-connect Node C

Figure 1: Virtual Paths shown for two dierent STQoS classes for a demand pair 23

3

10

2

1 8

6

4

7

Switching node Cross-connect node

5

9

Figure 2: Topology of EN-1 (7 ATM switching nodes, 10 ATM Cross-connect nodes)

Switching node

8 3

Cross-connect node 17

1

6

16 13

9

11

5 10 14 15 7

2

12

4 18

Figure 3: Topology of EN-2 (10 ATM switching nodes, 18 ATM Cross-connect nodes)

13 2

8 1

20

21

9

14

5

22

23

15 18 6

19 12

3

11

17

4 Switching node

7

16 10

Cross-connect node

Figure 4: Topology of EN-3 (15 ATM switching nodes, 23 ATM Cross-connect nodes)

24