A multiple criteria model for the allocation of data files in a distributed information system

Compurers Ops Res. Vol. 19, No. 1, pp. 21-33, 1992

0305-0548/92

Printed in Great Britain. All rights reserved

$5.00 + 0.00

Copyright 0 1992Pergamon Press plc

A MULTIPLE CRITERIA MODEL FOR THE ALLOCATION OF DATA FILES IN A DISTRIBUTED INFORMATION SYSTEM HEESEOK LBB’t and OLIVIA R. LIU SHENG~$ ‘Department of Computer Science and Information Systems, Moorhead State University, Moorhead, MN 56563 and ‘Department of Management Information Systems, University of Arizona, Tucson, AZ 85721, U.S.A. (Received January 1990; in revised form August 1991)

Scope and Purpose-The file allocation problem to determine the allocation of data files in distributed computer systems has been extensively studied in the literature. This problem has been known to be complex and challenging because of a variety of design settings. The major objective of this paper is to present a multiple criteria formulation of the file allocation problem in which design objectives are often in conflict. A computational procedure for the resulting difficult problem is further explored. Abstract-This paper addresses a multiple objective optimization model to determine the file allocation and query routing assignment in a distributed information system. The problem is formulated as a zero-one integer nonlinear programming problem with multiple objectives. The optimization problem under consideration is shown to be NP-hard. We adopt an iterative improvement procedure, which gives the Pareto optimal solution. We further illustrate our methodology with a small sample system. 1.

INTRODUCTION

Advances in integrated logic and communication technology coupled with the decreasing costs of computers have made distributed information systems emerging alternatives for modern information services. Distributed information systems consist of a collection of computing sites interconnected by a communication network. Each computing site has its own processing, storage and communication devices as well as the appropriate software resources. The interconnection can be provided by a wide-area network (WAN) for large geographical regions typically with a radius of larger than tens of kilometers, or by a local-area network (LAN) for a limited geographical area like a cluster of buildings. The WAN is typically of point-to-point topology to contrast it with the LAN, which usually has a broadcasting architecture. In point-to-point channels, the network contains numerous cables or leased telephone lines, each one connecting a pair of IMPS (interface message processors). Broadcast systems, however, have a single communication channel that is shared by all machines on the network. Readers are referred to [l] for a detailed description of the communications network. It has been noted that distributed information systems involve several complicated design issues such as distribution design of databases, concurrency control, query optimization, subnetworks design, etc. For further discussion of such issues, see for example [2]. In this paper, we focus on the distribution design of databases connected by the WAN. The design of centralized databases includes conceptual schema design and physical database configuration. In distributed databases, these two problems can be solved in the same fashion as in centralized databases. The distribution of databases, however, involves two new problems : the partitioning of the global tHeeseok (Andrew) Lee received the B.S. in Industrial Engineering from Seoul National University, the MS. in Industrial Engineering from Korea Advanced Institute of Science and Technology and the Ph.D. in Business Administration from the University of Arizona. Dr Lee is an Assistant Professor of Computer Information Systems at Moorhead State University. His current research interests include database design, distributed information systems, data communication networks and software engineering. His papers have been published in Computers & Operations Research, Computers & Industrial Engineering, Annals of Operations Research and Systems Science. $Olivia R. Liu Sheng is an Assistant Professor of MIS at the University of Arizona. She holds an MS. and Ph.D. in Computers and Information Systems from the University of Rochester. Dr Sheng’s principle research interests are analysis and design of distributed information systems. Other current work focuses on developing optimization models and integration, design of office information systems and image database systems, data modeling, an expert systems approach to automation of database design and computer mediated coordination. 21

22

HEESEOKLEE and OLIVIAR. Lru

SHENG

database into physically and logically separable fragments and the allocation of these fragments possibly along with their replicas to computing sites on networks. Both problems are related to each other since how the database is partitioned will affect and be affected by how the partitioned fragments will be allocated. In [ 31, it is noted that the database partitioning scheme and fragment allocation can be one and the same decision under a specific database access pattern assumed. Yet solving both problems simultaneously is complex in general cases. Previous research has tackled only one problem assuming that the other is determined a priori. Several methodological approaches to the database partitioning have been investigated in a number of sources (e.g. see [4] and [ 51). The problem of the allocation of the partitioned fragments especially on the WAN is known as the file allocation problem in the literature. Most file allocation work has been concerned with a single criterion in isolation; either minimization of overall operating costs or optimization of some performance-related measurements. Various file allocation models have been formulated as combinatorial problems so that the sum of data storage and communication costs is optimized with linear constraints (e.g. see [6-lo]). Q ueuing network models have been adopted when either minimization of system response time or maximization of throughput is the primary performance measure of interest (e.g. see [ 1l-141). For a comprehensive review of the file allocation problem, see [ 151 and/or [ 161. The file allocation model reported in this paper differs from previous ones in the sense that multiple objectives that are often in conflict are considered. We consider three important optimization criteria such as operating cost, system response time and availability. Such three criteria optimization models in the context of the distributed computer systems have been reported in [ 171 and [ 181. A bicriterion optimization model especially in a local environment can be found in [ 19J. We further advance these research works within the framework of file allocation’and query routing assignment under multiple design objectives. The problem is to allocate replicated copies of files to geographically dispersed sites in this multiple criteria environment. Incorporating the trade-offs among conflicting objectives is likely to yield more realistic design than traditional methods addressing a single objective in isolation. The rest of the paper is organized as follows. The next section describes the system under study and introduces the notation. A multiple objective optimization formulation of the problem is presented in Section 3. Section 4 outlines the characteristics of the problem followed by a solution procedure employing a simple exchange heuristic. In Section 5, a numerical example is solved to illustrate the method. Section 6 concludes this paper.

2. SYSTEM

DESCRIPTION

AND

NOTATION

As observed in the previous section, the distribution design of databases in a distributed information system can be fully characterized by two problems as follows [20] : (i) Designing the fragmentation of database, i.e. the partitioning database into fragments. (ii) Allocation of the fragments to processing nodes on networks.

of the central

The data model in distributed information systems is almost invariably the relational model [2 11. This choice is appropriate because links in a hierarchical or a network model are too complex to utilize and maintain in distributed databases and remote links are not as useful as local links. In contrast, the relational model employs the powerful set-oriented, assocative expressions that have been shown to be useful and convenient in distributed databases. In the relational model, data are stored in tables, called relations. Each relation has a number of columns, called attributes, and a number of rows, called tuples. The purpose of fragmentation is to determine nonoverlapping units of allocation for the subsequent design phase. The set of horizontal fragments consisting of subsets of the tuples of the relation is a good candidate for such a decomposition. The fragments produced by this fragmentation can be referred to as data files. Such data files are appropriate units of allocation. A particular strategy of fragmentation defines how its respective data files are to be distributed over geographically dispersed processing nodes. Hence, if we assume the design of fragmentation is previously defined, the problem is simply reduced to allocating data files so that the overall

23

A multiplecriteriamodelfor data file allocation

desirability of the system for a given fragmentation design is optimized. This paper concentrates on such a problem. File requests include queries and updates. A query requests data retrieval only. However, an update requires the modification of current data content. A major difference between query and update can be illustrated in the case of data replication. While a query reads a single data element having the information requested, an update must reference and write all of the data elements which contain the information to be updated. Such a scheme for handling multiple copies in distributed databases can be referred to as read one and write all (ROWA). Request routing algorithms can be grouped into two major classes: static (nonadaptive) and dynamic (adaptive) [22]. A dynamic algorithm attempts to change its routing to reflect short-term fluctuations of request arrival. A static algorithm, on the other hand, does not base its routing assignments on measurements or estimates of the current traffic and topology. Its goal is to optimize the average system performance measure, averaged over statistically varying measures resulting from fluctuation in a long run. A static policy is simple to implement and maintain while a dynamic policy involves a significant communication overhead. In this paper, we confine ourselves to static policies. Typically, we can describe the system operation as follows. A file request is locally processed if the data items are resident at that node; otherwise, the request is directed to the processing node which has the data file containing data items requested. For this purpose, the request traverses and queues for the channels. Finally, the request receives file service and exits the system. We now define a decision variable Xrj to describe the allocation of each file to processing nodes : X,j =

1, if file I is allocated to node j ; 1 0,

otherwise.

We further define another decision variable Yrkjfor determining the fashion in which the query is routed to the node where the file requested is resident: y

= IkJ i

1,

if the query request for file I arriving at node k is routed to node j

0,

otherwise.

;

The following notation is used to formulate the problem under consideration: F = total number of data files N = total number of processing nodes M = total number of channels in the communications network 3, = total rate of file requests entering the system y = total rate of file requests in the system Au = the average rate of requests of file I arriving at node j tllj = the average rate of query requests of file I arriving at node j flu = the average rate of update requests of file I arriving at node j ykj = the average rate of file requests from node k to node j qlkj = the communication cost of transmitting the query request of file I from node k to node j and transmitting the reply from node j back to node k ulkj = the communication cost of transmitting update request of file 1 from node k to node j slj = the storage cost of the file I at the processing node j K = the average nodal delay of packet 1/p = the average length of packet (i.e. the average size of file request) Bi = the capacity of channel i dl = the size of file 1 oi = the storage capacity of node i rij = the probability that node i can communicate node j r, = the reliability of node i. 3. PROBLEM FORMULATION We assume that files are designated by a particular fragmentation design. Multiple copies of files are allowed. Transaction requests consist of updates and queries. Let us consider the point-to-point IZcs 19:1-B*

HEISEOKLEE and OLIWA R. LIU SHENG

24

WAN with M channels. The designer should optimize the allocation of F files over N geographically dispersed nodes. The problem under consideration is determining how to allocate files and assign queries when multiple design objectives are in conflict. In other words, the model should determine file allocation and query routing for a given fragmentation design. The concentration is on the three design objectives (operating cost, system response time and availability). The model should consider trade-offs among the three design objectives. For instance, we can reduce the operating cost by putting an entire database at one computing site where it is cost-effective for the system to access data and operate upon it. However, concentrating a large volume of the database at one processing node may mean that a correspondingly large number of requests will be directed to that site, which results in increased system response time. Obviously, this strategy also reduces availability. We now introduce three design objectives and express them analytically, using the notation X, for file allocation and/or Yrkjfor query routing assignment. 3.1. Operating cast evaluation The operating cost under consideration contains both storage costs and communication costs. Storage costs include costs incurred by the storage and operation of data at a local site. communication costs are costs by transaction transfer between sites. Since file requests may result in updating a local or remote file, the expected communication costs include query communication cost and update communication cost. The expected communication cost C, is simply computed as the sum of the individual communication costs as follows:

1

alk91kjY,kj

C

+

PIkUkjXlj

k#j

k#i

1 *

In addition, storage cost is computed by C, = ~

~ SljX,j.

I=1 j=l

The storage costs may be ignored since communication costs dominate due to the fairly long distance between source and destination for a WAN. In this research, we have incorporated the storage costs in our model. Thus the overall operating cost is represented as y~

=

cc

+

cs

=

i

2

1

I=1

j=l

kfj

alkqlkjylkj

+

c

blkUlkj

k#j

+

slj

xlj >

1 3

or equivalently, y~ =

f: f? 1=1 j=l

[

C k#j

(1)

@lkqlkjYlkj + d,jX,j],

where

d,j = C

PIk%kj

+

Slj,

Vl=

1,. ..,F,j=l,...,

N.

k#j

Here, d, can be interpreted as the operating cost of file 1 at node j. 3.2. Response time evaluation Data are replicated for two main reasons: availability and read performance. If the files are appropriately located, then database access can be executed more effectively, possibly avoiding costly communications. If there are redundant copies of a file then that file can be accessed even when some of the processing nodes that hold copies fail. Therefore, we consider two measures of ~rformance in addition to operating cost : system response time and availability. In order to examine response time, let us consider the distributed computer system as an M-channel, N-node packet switching network (see for reference [23] and/or [24]). Such a

25

A multiple criteria model for data file allocation

point-to-point network is characterized by a queue to represent each direction of each transmission link (full duplex ). The service at a queue is the actual transmission of the packet and is proportional to the size of the packet. A common assumption is that requests arriving at a particular site can be represented by Poisson processes. In consequence, the total traffic intensity entering the system can be represented by

I=1 k=l

(2)

1=1 k=l

In order to find the mean request flow on each channel, we compute a request arrival originating from node k and destined for node j that forms a Poisson process with rate ykj

Ykj

=

i I=1

(%kylkj

+

:

Vk#j=l,...,N.

flIkXIjh

The total traffic intensity in the system is

5 ('%k +1

Y = f: I=1

k=l

(3)

Xljblk),

j#k

because update requests must be transferred to all nodes which contain the information to be updated. Assuming that the query/update routing has previously been defined, we may denote the path taken by messages that originate from node j and are destined for node k by nkj. The channel i is included in the path nkj if the channel is traversed by messages following this path. In such a case we adopt the notation i E zkj, Then the mean rate of request flow Cpion channel i equals the sum of the mean request flow rates of all paths that traverse this channel, i.e. +i

=

1

k,j

imtk,

Ykj

=

c k,j iam,

i I=1

falk&kj

+

plkxIjh

Vi=l,...,M.

(4)

A performance measure of interest is the average time spent in the system by a file request. We have Y’,to denote this random variable. As discussed earlier, Y, consists of the node delay (processing and queuing delay) and the communication delay incurred by request transfers. We denote the average nodal delay to process a file request by K. We now come to compute the communication delay. For the sake of analytical tractability, we do not disinguish between the service times for queries and updates. All requests are assumed to have lengths that can be approximated by exponential random variables with mean l/cl. In other words, l/p is the average length of a file request (bits). Since the request arrival at channel i forms a Poisson process, the channel i can be represented as an M/M/l queue with request arrivals at rate 4i and has a mean service rate of ~Bi. The communication delay at channel i is given as follows: 1

Tsi = -, Mi

-

Vi=l,...,M. 4i

Therefore, the average system response time can be obtained by y

t

=K+

E +[T.+K]. St

i=l

Y

The one additional term K outside the brackets is necessary because requests pass through one more node than they do channels on the network. The above can be represented again:

In [22], it is further shown that so long as the overall traffic intensity y is in the stable region,

26

HEEBOIC LEE and OLIVIAR. LIU SHENO

the average system response time can simply be reduced to

y=K+Fi t i=l

‘+x Y [

1

Hi

’

or equivalently,

(5) This objective is nonlinear with respect to file allocation. We adopt this response time evaluation in our multiple objective formulation. 3.3. Av~iI~~iliiy evaluation Due to the failures of processing node and/or transmission links in WAN, certain file requests (transactions) may be lost at a particular point of time, Availability in distributed information systems is defined as the fraction of file requests which complete, on time, out of all the file requests that are submitted to the system [25]. The expression for such a system-wide availability, W,, can be derived on the basis of network reliabilities as follows. Given the failure probabilities (reliabilities) for the nodes and links, the values of certain measures of network reliability can be computed. Nodes and links can be in either of two states : operative or failed. The probability that all operative node pairs can communicate has been referred to as network reliability. In contrast, the sours-destination reliability in computer network is the probability that two nodes (source and destination) can communi~te. Two nodes can communicate if they are both operative and if there is a path containing operative nodes and links between them. In other words, source-destination reliability rjj between node i and nodej can be formally defined as the probability that node i can communicate with nodej. Efficient algorithms have been developed for computing these values (see for example [ 261). We focus on source-destination reliability rather than network reliability as a whole since it, along with query routing assignment, provides a more accurate result and the other probabilities can be derived from it. Availability evaluation varies depending upon query and update since their routing in the networks are different. If the queries which request the file f arrive at site j with a mean rate of Cl*j,the probability that these requests are complete is X,rj if X, = 1; otherwise the probability is Ckf j Hence, the query availability can be represented by Yzkrjk.

1F A@= - C

N C

a I=1 j=l

alj

C

1

yljkrjk + X,jrj .

kfj

Note that total rates of query request and update request are 0: = XI xj alj and p = & Cj blj, respectively. An update request is complete if all updates transferred to sites that contain data items to be modified are successfully executed. Hence the update availability is

In

consequence, the system-wide availability can be summarized as ‘I‘, = w,A, + wpAa,

or equivalently, ‘lj

c k#j

%jkrjk

+ xljrj

1

+ F

,fl

j$l

plj

7

rjkq

Xlk=l

For convenience, we denote 5 by rjj. The designer has the responsibility to assign relative weights w, and w8.

A multiple

criteria

model for data file allocation

Table 1. Optimization criteria and objectives in a fik allocation orobkm Optimization criteria

Objectives

Operating cost (Y,) System response time (P,) Ava~Iability fYY,)

Minimize operating cost Minimize system response time Maximize availability

This availability model is more accurate than an approximate model by Irani and Khabbaz [27], whose model assumes that the computer network is highly reliable. Their model is based on network reliability rather than source-destination reliability. Their model evaluates availability on files rather than on transactions. 3.4. A multiple objective formulation The mathematical expressions for three optimization criteria have been developed thus far. It is not surprising to discover that, considered separately, these optimization criteria may suggest different strategies of file allocation and query routing assignment. The purpose of our model is to optimize overall desirability of different strategies of file allocation and query routing assignment. In multiple objective decision making, each objective indicates the direction which the system designer should strive at the expense of achievement on the other objectives. We summarize the relationship between the optimization criteria and the corresponding objectives in Table 1. For the completeness of the model, we introduce the system constraints to generate the feasible solutions as below. We first consider the constraints on file copies. Since there is at least one copy of each file we have

$ x,j>l*

VI=l,...,F.

(7)

j=i

The query request at node k will be satisfied by accessing a file at some nodes. And if the query originates at the nodes where the file is resident, then the query request will be satisfied at that node. Thus, C Y&j$X,,=l, .i#k

Vl= l,...,F,k=l,*.*,N*

(8)

Since a copy of the file at node k can be routed to node j only if there exists a copy of the file at node j, we have Ylkj< x,j,

Vl=l,.,.,

F,k=l,...,

N,j=l,...,

N,k#j.

(9)

In addition to the three feasibility constraints above, we provide two more constraints (stability and storage capacity constraints). The communication network is not stable if one of the channels is saturated. To avoid the saturation of each channel, the stability constraint can be written as (bi < ~Bi, Vi =: 1, . . ., M, or equivalently for a given number E, g

~~~(r,Y*kj+~~kX,i)+&GPBi,

Vi=l,...,M.

(10)

isnrj Too small a value of E may cause an unexpected system performance. For the choice of the value of E, see for example [23] and [28]. Finally, in order to satisfy the storage capacity of each node, it is required that i d,X,j 1=1

<

Oj,

Vj = 1, . . . , N.

(11)

The general multiple objective optimization formulation is described in a number of sources (e.g. see [29-321). For combinatorial problems, a common multi-criteria formulation technique

HEESEOKLEE and OLIVIA R. LIU SHENG

28

has been a vector minimization. We denote our decision variables by a vector

We can then present the vector minimization formulation of the design problem as below : Model FAP-MO

min

Ye =fc(z)

min

y, =L(z)

max

y, =f.(z)

s.t.

zES,andz=(O,l).

The above model has been referred to as the file allocation problem under multiple objectives (FAP-MO). The objective functions f,, f, and f,, correspond to equations (l), (5) and (6), respectively. Note that f, and f, are nonlinear, but f, is a linear function of z. The constraint set S, consists of equations (3), (7), (8), (9), (10) and (11). The FAP-MO can fall into the class of zero-one integer nonlinear programming problems with multiple objectives. 3.5. Model comparison In the Introduction, two file allocation models for WAN under multiple objectives (Jain and Dutta [ 173 and Jain [ 181) have been introduced. Both models solve for file allocation as a part of the overall distributed computing design. For instance, Jain’s model [18] determined processor assignment as well as file allocation. However, query routing assignments are not incorporated in these models. In contrast, the FAP-MO solves for file allocation decision and query routing assignment. Furthermore, these models adopt different evaluation methods for design objectives. Key aspects of these three models are compared in Table 2. The FAP-MO has several advantages in modeling if the designer is to solve for file allocation decision only. The FAP-MO incorporates the query routing assignment decision which is related to the file allocation decision. The FAP-MO evaluates design objectives more accurately. For instance, the expression for availability is exactly based on source-destination reliabilities, comparing with approximate expression of the other models. Furthermore, the FAP-MO defines availability based on transactions rather than fragments, which is more appropriate in distributed information systems. Operating costs are expressed by both file allocation and query routing decisions. Furthermore, the response time is assessed through system parameters according to a standard queuing system.

Table 2. A comparison for file allocation models under multiple objectives Modeling aspect

Jain/Dutta

[ 177

Operating costs

No evaluation

Response time

A computational procedure adopted for a given file allocation Irani and Khabbaz’s [27] file availability evaluation that is approximately based on network reliability File allocation Network topology Processor assignment

Availability

Decision variables

Jain [lS]

FAP-MO

Communication costs based on file allocation Linear model (A + B x load) Same as [ 171

Communication cost based on file allocation and query routing Measured by M/M J 1 queues

File allocation Processor assignment

File allocation Query routing

Exactly based on source-destination reliability

29

A multiple criteria mode1 for data file allocation 4. A SOLUTION

PROCEDURE

Due to the presence of additional objectives and constraints, the FAP-MO is considerably more difficult to solve than conventional file allocation models. The computational complexity of the problem is outlined as follows. Proposition 1

The FAP-MO is NP-hard. Proof. (By restriction.) d’ such that

The decision problem of the FAP-MO is to find the constants c’, t’ and

f,(z) < c’,ft(z)

< t’,fd(z) 2 d’, z E S, and z = (0, 11.

We can consider a specific instance of the above decision problem such that F=l,t’=~1,d’=O,0~=~,Vi=l,...,

Mandwi=~,Vi=l,,..,

N.

Solving this problem then is equivalent to solving the well known file allocation decision problem. But the file allocation decision problem is NP-complete. For a proof, see for example [33]. Hence the corresponding optimization problem is NP-hard [34]. For a problem of realistic size, it is not possible to find the solution in acceptable time. Therefore, heuristic algorithms or problem reducing techniques which take advantage of the problem structure are needed for solving the FAP-MO. An adaptive search procedure (see for example I:17) ) is employed for this purpose. We adopted this methodology in view of its flexibility to examine alternatives. The method is of a highly interactive nature, which enables the human system designer to decide the Pareto optimum. The human system designer can easily explore many possible designs until a final compromised solution is reached. Additional objectives can also be incorporated without major revision of the method. For this purpose, an exchange heuristic [35] may be employed to generate the sequence of solutions z”, zl, . . ., until a compromised solution z* is reached. The basic premise of the exchange heuristic is that some variables are in solution while others are out of solution and certain exchanges of one or more variables in solution for one or more variables out of solution are examined. Here some components of z are set to 1 while others are set to 0. The heuristic exchanges the values of one or more variables with a value of 1 for one or more variables with a value of 0. In this manner, the exchange search heuristic systematically finds nondominated solutions. The adaptive search procedure requires an initial feasible solution, say, z” E S,. We need to solve single objective problems to generate and select an initial feasible solution. We need to solve the three single objective problems regarding operating cost, response time and availability, respectively, i.e. (1) minimizing Y’, subject to z E S, and z = {0, l}, (2) minimizing Y, subject to z E S, and z=~O,l)and(3)maximizingY,subjecttoz~S,andz=(O,l). Here, minimi~ng Y, and maximizing Y, are not trivial tasks due to their nonlinearity, Alternatively, we may adopt the following linear objectives because we only need a near-optimal solution for a starting point. Instead of minimizing Y, directly, we may minimize the following quantity ~=~~[~+~]x[

5

,cl

@d&

+

PtkXlj)

.

, ifrCkj

1

Note that the quantity q is the total amount of traffic intensity while mean request flow rates on channels are adjusted by their processing capacities. Similarly, we may maximize Y’, assuming wB= 0. This provides a good solution because in most systems the number of query requests dominates the number of update requests. After obtaining the solutions, we compute the corresponding response time Y: and Y,* by equations (5) and (6), respectively. To solve for the aforementioned three single objective problems, we use the ZOOM system described in [ 361 and [37]. The ZOOM system has been successfully used in solving the file allocation problem with a single objective (see for example [ lo] and [38] ). The ZOOM system is commercial software for general purpose mixed-integer programming problems with no special

30

HEESEOK LEE and OLIVIA R. LIU SHENG

structure. The ZOOM system is intended for up to about 200 zero-one variables so that it can handle, for instance, a lo-file 20-node FAP-MO. This is a reasonable problem size we can expect for realistic systems. The initial solutions obtained thus far for single objective problems represent extreme nondominated solutions to the original multiple criteria problem. One of these three solutions may be selected as the starting solution. The designer’s preferred solution is expected to lie in a space bounded by these solutions so that a positive weighted sum of single objectives is maximized [39]. This solution is referred to as a Pareto optimal solution in the area of multiple criteria decision making. The compromise solution is expected to move toward such a Pareto optimal solution. At this stage, the procedure asks the designer to specify an acceptable region for objective function values. This region represents the trade-off of performance in each design objective that the system designer would be willing to pay to improve some other design objectives. A set of nondominated solutions within the acceptable region is found by the exchange search heuristic. This procedure improves the solution in an iterative manner until a Pareto solution is reached. 5. AN

ILLUSTRATIVE

EXAMPLE

To demonstrate the suitability of our model, let us consider a small sample system. The system is connected by a sample network. For convenience, this sample communication network will be called the Pacific Networks (PACNET), which is illustrated in Fig. 1. The network consists of six nodes (N = 6) and eight channels (M = 8). We consider a single file allocation problem on the PACNET. Table 3 gives the file access requirements, file storage cost and node reliability. Channel capacity and file communication cost are given in Table 4. Assume that enough storage capacity is provided at each processing node.

Legend 1 Seattle 2 San FkLncisco 3 Los Angeles 4 Las Vegas 5 San Diego 6 Phoenix Fig. 1. A proposed

topology

for PACNET.

Table 3. Node related data of PACNET

System parameter Total number Total number Total number

of files (F) of nodes (N) of channels (M) Request rate, nodes 1. .6 (Ali) Query request rate, nodes 1. .6 (ali) Update request rate, nodes 1. .6 (p,,) Storage cost, nodes 1, ,6 (sl,) Node reliability, nodes 1. .6 (rj)

Specification 1 6 8 10 4 8 4.5 11 8 (request/set) 8 3 6 3 9 6 (request/set) 2 1 2 1.5 2 2 (request/w) 3.33 6.67 30.0 20.0 3.33 16.67 ($/day) 0.95 0.955 0.99 0.975 0.985 0.98

31

A multiple criteria model for data file allocation Table 4. Communication

Channel

4 1, 1, 1, 1, 1, 1, 1s

cost and channel capacity of PACNET

Query cost (10-4S/sec)

Update cost (lo-‘%/set)

1.3 3.1 1.5 2.5 1.1 0.5 2.1 1.8

1.6 3.1 1.8 3.0 1.3 0.6 3.2 2.2

Table 5. Source-destination

Capacity (kilobits/sec) 19.2 9.6 19.2 4.8 19.2 50.0 19.2 19.2

reliability (q,) of PACNET Destination

Source

1

1

2 3 4 5 6

0.905 0.937 0.921 0.926 0.917

2

3

4

5

6

0.905

0.937 0.944 0.963 0.965 0.951

0.921 0.926 0.963

0.926 0.933 0.965 0.95 I

0.917 0.917 0.95 I 0.946 0.958

0.944 0.926 0.933 0.917

0.951 0.946

0;8

Table 6. Initial candidate file allocation on PACNET Min Y,

Objective Solution Yy, (%/month) Y, (set) y. (“/) Optimal file allocation Optimal query routing

a: 10,800 57.1 95.61 5 l-5 2-53-54-56-5

Min Y,

Max I,

a: 12,200 46.2 95.92 15 2-l 3-5 4-5 6-5

a: 26,700 51.3 91.36 123456 None

The average size of the packet (request) is 64 bytes. The designer decides to concentrate on maximizing the query availability (i.e. w, = 1 and wg = 0). We assume that the node delay is much smaller than the communication delay and is thus ignored (K = 0). The calculation is based on the computer being in operation 100 h per week and 4.2 weeks per month. The communication cost between two processing nodes can be represented by the sum of cost terms of channels traversed by the path. Source-destination reliability has been computed according to node reliability and channel reliability and is presented as Table 5. For each of the initial feasible solutions obtained, we can compute the values of the remaining two objectives. Actually the ZOOM system can generate these values while optimizing the objective of major interest. The operating cost is assessed in terms of monthly operating cost. Table 6 lists the results. For instance, column 1 in Table 6 gives the solution vector I$ which minimizes the operating cost. This solution corresponds to the optimum obtained by the file allocation with the minimization of costs in isolation. The file allocation problem may be referred to as file allocation problem with a single objective (FAP-SO). Thus the FAP-SO can only optimize the operating cost irrespective of the other design objectives. Assume that the system designer selects z; from Table 6 as the starting solution and is willing to pay up to $10,000 more in terms of operating cost in exchange for improving the system response time and/or availability. Then the exchange heuristic generates the solutions in the following acceptable region : operating cost up to $110,000 system response time up to 50.0 set availability up to 96.00%. All nondominated solutions within this region will be accepted as current feasible solutions. If none of these solutions is satisfactory, the designer chooses a new starting solution; otherwise, the

32

HEE~~OKLEE and OLIVIAR. LIU SHENG Table 7. Comparison

between optimal tile allocation by FAP-SO and Pareto optimal file allocation by FAP-MO

Model values File allocation, nodes 1 6 Query routing assignment Operating cost (%/month) Response time (SW) Availability (%)

FAP-SO 5 l-5 2-5 3-54-56-5 10,800 57.1 95.61

FAP-MO 15 2-13-54-56-5 12,200 46.2 95.92

designer reaches the Pareto optimal solution. The system designer may change the starting solution and/or acceptable region assigned to generate alternative designs. We continue the process and finally obtain the compromise solution (Pareto optimum) as in Table 7. Table 7 also highlights the advantage of the model FAP-MO over the single objective model FAP-SO. The operating cost can be reduced to $10,800 per month by adopting a single objective model FAP-SO. However, the system designer feels that the response time is not satisfactory in this case. Table 7 shows how the response time is improved to the detriment of operating cost. In addition, availability is improved. The file allocation and query routing assignments change accordingly. In this example, the compromise solution corresponds to one of the initial candidate solutions which optimizes the response time in isolation. In most cases, however, the compromise optimum lies in a space strictly bounded by three initial candidate solutions. 6. CONCLUDING

REMARKS

In this paper, a compromise among conflicting objectives in determining file allocation and query routing assignment in a distributed information system has been explicitly acknowledged. Three design criteria of major interest are introduced and a multiple objective optimization formulation is presented. An interactive solution procedure employing an exchange heuristic is then used to determine the acceptable file allocation and query routing assignment simultaneously. To demonstrate the feasibility of our methodology, we solve a small sample system. This method is more likely to provide a better solution to the file allocation problem than the single objective models which have been widely adopted in the literature. It is hoped that the model of this paper will provide a useful instrument for other computer system designs. REFERENCES 1. W. Stalling, Data and Compurer Communications. Macmillan, New York (1988). 2. J. Martin, Design and Strategy for Distributed Duru Processing. Prentice-Hall, Englewood ClifIs, N.J. (1981). 3. H. Lee and 0. R. Liu Sheng, Optimal data allocation in a bus computer network. In Proc. Ninth IEEE Co& Computers Commun., pp. 394-399 (1990). 4. S-K. Chang and W-H. Cheng, A methodology for structured database decomposition. IEEE Trans. Sofiwure Engng SE6,205-218 (1980). 5. S. Ceri, B. Pernici and G. Wiederhold, Distributed database design methodologies. Proc. IEEE 75, 533-546 (1987). 6. W. W. Chu, Optimal file allocation in a computer network. IEEE Trans. Computers Cl&I, 885-888 (1969). 7. R. G. Casey, Allocation of copies of a file in an information network. In Proc. AFZPS Spring Joinr Computer Conf., Vol. 40, pp. 617-625. AFIPS Press, Montvale, N.J. (1972). 8. H. L. Morgan and K. D. Levin, Optimal program and data locations in computer networks. Commun. ACM 20, 315-322 (1977). 9. H. Pirkul, An integer programming model for the allocation of database in a distributed computer system. Eur. J. Ops Res. 26, 401-411 (1986). 10. S. Ram and R. E. Marsten, A model for database allocation incorporating a concurrency control mechanism. Working Paper, Department of Management Information Systems, University of Arizona, Tucson, Ariz. (1988). 11. P. P. S. Chen, Optimal file allocation in multilevel storage systems. In Proc. AFZPS National Computer Co& Vol. 42, pp. 277-282. AFIPS Press, Arlington, Va (1973). 12. D. V. Foster, L. W. Dowdy and J. E. Ames, File assignment in a computer network. Computer Network S,341-349 (1981). queuing network optimization approach. Computers 13. M. M. Srinivasan and K. Kant, The file allocation problem-a Ops Res. 14, 349-361

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