## Time and cost tradeoff for distributed data processing (1989)

Venue: | Computers ind. Engng |

Citations: | 3 - 1 self |

### BibTeX

@ARTICLE{Lee89timeand,

author = {Heeseok Lee},

title = {Time and cost tradeoff for distributed data processing},

journal = {Computers ind. Engng},

year = {1989},

volume = {16},

pages = {553--558}

}

### OpenURL

### Abstract

Abstract--An important design issue in distributed data processing systems is to determine optimal data distribution. The problem requires a tradeoff between time and cost. For instance, quick response time conflicts with low cost. The paper addresses the data distribution problem in this conflicting environment. A formulation of the problem as a non-linear program is developed. An algorithm employing a simple search procedure is presented, which gives an optimal data distribution. An example is solved to illustrate the method.

### Citations

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Citation Context ...efine the auxiliary function X~(2) as follows: And also define The X(2) is monotonically increasing in 2, where X i .-~. -Y - -- -- 7 qJ,-dr' ! Vi = 1, . , . N. (17) # X,(2) = #--' 1 / x#i Vi = 1, N. =-=(18)-=- Y 7 X/ 2 - di N X(2) = ~ X~(2). (19) i=1 2 > max d~. (20) i6l The monotonicity of X(2) implies that we can easily calculate 2 numerically so that X~(2) = 1, thus implying that the constraint (1) is s... |

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Citation Context ...mmunication cost is minimized. Queueing models have focused mainly on minimal response time as a criterion of performance [9-11]. A comprehensive review of the file allocation problem can be found in =-=[12]-=-. Typically, one of two optimization objectives has been adopted in the design of distributed data processing systems: either minimization of overall operating cost or optimization of some performance... |

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Citation Context ...verage time spent in the system by a file request. Denoting this random variable by T, we can see that T can be obtained as the weighted sum of response time of each node simply using Little's result =-=[14]-=-: T= L 7g L. (4) The g includes the request processing time, the delay times resulting from the processing of file request, and the computer access time. In most cases, the computer access time is muc... |

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Citation Context ...ertain advantages depending upon the manner in which data are distributed. The distribution of data can be fully characterized by two problems: designing the fragmentation and allocation of fragments =-=[1]-=-. Fragmentation design has rarely been studied. Some methodological approaches are presented in [2, 3]. On the other hand, the allocation of fragments has been widely analyzed in the context of the fi... |

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Citation Context ... been studied. Some methodological approaches are presented in [2, 3]. On the other hand, the allocation of fragments has been widely analyzed in the context of the file allocation problem, since Chu =-=[4]-=- originally investigated the file allocation on a multi-processor system. In [5-8], the objective of the problem is to allocate copies of data files to processing nodes so that the sum of data storage... |

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Citation Context ... Combined with the fact that the arrival process concerning ?~ in (3) is a Poisson process, each processing node can be modeled as M/M/I queue [15] in an open central server network so that Ti = --.l =-=(5)-=- #~- 7 x~ (1)sTime and cost tradeoff 555 To prevent the queue lengths from growing without bound, it is required that xi <l~, Vi= l ..... N (6) ? that is, the mean rate of requests transmitted to a pa... |

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Citation Context ...iew of the tradeoff between system response time and operating cost. SYSTEM ANALYSIS AND MODEL FORMULATION An information system in distributed data processing systems is almost invariably relational =-=[13]-=- due to its simplicity of fragmentation. In this case, the information system is a common, global relation itself. The relation is just a mathematical term for a table consisting of tuples and attribu... |

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Citation Context ... l ..... N (6) ? that is, the mean rate of requests transmitted to a particular node must be less than the mean file service rate. From (4) and (5), the system response time is N T= x, e= l/~i - ?xi" =-=(7)-=- We can express the operating cost in terms of the data distribution x~. The operating cost consists of storage cost and communication cost. The expected storage cost per unit time is N S = Y, six e. ... |

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Citation Context ...[15] in an open central server network so that Ti = --.l (5) #~- 7 x~ (1)sTime and cost tradeoff 555 To prevent the queue lengths from growing without bound, it is required that xi <l~, Vi= l ..... N =-=(6)-=- ? that is, the mean rate of requests transmitted to a particular node must be less than the mean file service rate. From (4) and (5), the system response time is N T= x, e= l/~i - ?xi" (7) We can exp... |

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Citation Context ...equest is an exponential random variable with mean 1//~i. Combined with the fact that the arrival process concerning ?~ in (3) is a Poisson process, each processing node can be modeled as M/M/I queue =-=[15]-=- in an open central server network so that Ti = --.l (5) #~- 7 x~ (1)sTime and cost tradeoff 555 To prevent the queue lengths from growing without bound, it is required that xi <l~, Vi= l ..... N (6) ... |

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Citation Context ... can be fully characterized by two problems: designing the fragmentation and allocation of fragments [1]. Fragmentation design has rarely been studied. Some methodological approaches are presented in =-=[2, 3]-=-. On the other hand, the allocation of fragments has been widely analyzed in the context of the file allocation problem, since Chu [4] originally investigated the file allocation on a multi-processor ... |

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Optimal file allocation in multi-level storage systems
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Citation Context ... is simply computed as Accordingly, the expected communication cost per unit time is Therefore the expected operating cost per unit time is or denoting se + ci by de, 1 N ce = ~j~= (~tjqj~ + fljuj,). =-=(9)-=- N a = ~ CiX i. (10) i=l N C = S + Q = ~, (s,+ G)Xe, (1 1) e=l N C = ~ dixe. (12) i=l Here de is the operating cost incurred at node i. From (7) and (12), it is pointed out that each of the two cost f... |

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Nonlinear Programming, A Unified Approach.Prentice-Hall
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Citation Context ... follows: And also define The X(2) is monotonically increasing in 2, where X i .-~. -Y - -- -- 7 qJ,-dr' ! Vi = 1, . , . N. (17) # X,(2) = #--' 1 / x#i Vi = 1, N. (18) Y 7 X/ 2 - di N X(2) = ~ X~(2). =-=(19)-=- i=1 2 > max d~. (20) i6l The monotonicity of X(2) implies that we can easily calculate 2 numerically so that X~(2) = 1, thus implying that the constraint (1) is satisfied. In this case, a search proc... |

7 |
Introduction to Numerical Computations
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Citation Context ...notonicity of X(2) implies that we can easily calculate 2 numerically so that X~(2) = 1, thus implying that the constraint (1) is satisfied. In this case, a search procedure like the bisection method =-=[17]-=- can be used. The corresponding values of xi are then obtained from (17). The constraint (6) is always true of any values of x~ in (17). Hence the only way the set of x~ is not optimal is if one or mo... |

6 |
An integer programming model for the allocation of databases in a distributed computer system, European
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Citation Context ... We can express the operating cost in terms of the data distribution x~. The operating cost consists of storage cost and communication cost. The expected storage cost per unit time is N S = Y, six e. =-=(8)-=- /=1 Since the file request arriving at a node may result in updating a local or remote data file, the expected communication costs include query communication cost and update communication cost. Let ... |

3 |
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(Show Context)
Citation Context ... can be fully characterized by two problems: designing the fragmentation and allocation of fragments [1]. Fragmentation design has rarely been studied. Some methodological approaches are presented in =-=[2, 3]-=-. On the other hand, the allocation of fragments has been widely analyzed in the context of the file allocation problem, since Chu [4] originally investigated the file allocation on a multi-processor ... |

1 | The file allocation problem--a queueing network optimization approach - Srinivasan, Kant - 1987 |

1 |
A simple method to solve simple allocation problems, liE Trans
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Citation Context ..., Vi = 1 ..... N. (15)s556 HEESEOK LEE OPTIMAL DATA DISTRIBUTION The optimal solution to the problem (15) is obtained as follows. Our analysis is based on the well-known results of Lagrangian duality =-=[16]-=-. Temporarily relaxing the constraint (6) and applying the Lagrange multiplier 2, then the Lagrangian problem is L = TC + 2 (I- ~ (16) Taking the partial derivative of L with respect to each xi and se... |