Reliability evaluation of a computer network in cloud computing environment subject to maintenance budget
Introduction
This paper proposes a performance indicator to evaluate the capability of a computer network in the cloud computing environment. In a cloud computing paradigm, information is stored or processed by servers on the internet and cached temporarily on clients [10]. In the cloud computing environment, resources (computing capacity, storage capacity, or network bandwidth) are provided by powerful servers which can be depicted as the “cloud”. Thus, clients’ requests can be accessed from anywhere in the world. To guarantee a good quality of service (QOS) in the cloud computing environment the computer network should be maintained, so as not to fall into a specific state whereby the cloud cannot provide sufficient capacity to satisfy the client’s demand d. Yeh [26] defines the maintenance cost as the amount needed to restore a network from its failed state back to its original state, where the failed state is that the network sends less than the given d units of data. That is, the edges (physical lines such as fiber optics or coaxial cables) in the computer network should be recovered to their highest capacities when only d units of data can be sent. However, transmission time is not considered in Yeh’s work in which the transmission time is an important measurement when sending data through a computer network, especially in the cloud computing environment.
The important measurement should be involved in a computer network is the transmission time. When data is transmitted through a computer network, it is necessary to select the shortest delayed path to shorten the transmission time [3], [9]. However, the flow of data transmission is not considered in these works. In order to find a path which is able to send a given amount of data from the source (a cloud computing center) to the sink (a set of clients) with minimum transmission time, Chen and Chin [6] proposed a version of the shortest path problem, which they called the quickest path problem. In such a problem, the capacity and the lead time are involved at each edge and they are both assumed to be deterministic [6], [12], [21], [22]. Variants of quickest path problems, such as the constrained quickest path problem [5], [7], the first k quickest path problem [8], [23], and the all-pairs quickest path problem [4], [14], are subsequently proposed. Thereafter, Lin [16] extends the quickest path problem to a stochastic-flow network case. Previous works, however, mainly concern the time attribute without considering the maintenance to retain the computer network with a sufficient capacity state.
For a practical computer network, the capacity of each edge should be stochastic due to failure, partial failure, or maintenance. That is, each edge has several possible capacities or states [13], [14], [15], [16], [17], [18], [19], [20], [24]. Therefore, the computer network characterized by such edges also has stochastic capacities and it is a typical stochastic-flow network [13], [14], [15], [16], [17], [18], [19], [20], [24]. From the perspective of stochastic-flow network, we construct the computer network in a cloud computing environment as shown in Fig. 1, in which edges represent transmission media (physical lines such as fiber optics or coaxial cables) while nodes represent transmission facilities (switches or routers).
In this paper, we focus on the probability that the computer network in a cloud computing environment can send d units of data from the source (a cloud computing center) to the sink (a set of clients) under both maintenance budget B and time constraint T. This probability is henceforth referred to as the system reliability, which is the performance indicator of the computer network. In order to shorten the transmission time, the data can be transmitted through k (k ⩾ 2) disjoint minimal paths (MPs) simultaneously, in which an MP is a path the proper subsets of which are no longer paths. Hence, the transmission time, maintenance budget, and stochastic capacity are considered in this paper. We first generate all minimal capacity vectors satisfying the time constraint T, and subsequently check if they satisfy the maintenance budget B or not. An adjusting procedure is adopted to elevate those unqualified capacity vectors the total costs of which exceed B instead of deleting them. A branch-and-bound approach is proposed to generate all (d,B,T)-MPs, the minimal capacity vectors fulfilling d, B, and T, and the corresponding system reliability is derived afterwards in terms of (d,B,T)-MPs by the Recursive Sum of Disjoint Products (RSDP) algorithm. The remainder of this paper is organized as follows. Notations, nomenclatures, assumptions, and the computer network model are described in Section 2. Algorithm to derive the (d,B,T)-MPs and the system reliability are both proposed in Section 3. An example presented in Section 4 illustrates the algorithm and how the system reliability may be calculated. Discussion and conclusion are summarized in Section 5.
Section snippets
Assumptions, nomenclatures and acronyms
Let G = (S, E, W, C, L) denote a computer network in the cloud computing environment with a source (a cloud computing center) Scloud and a sink (a set of clients) Sclient where S represents the set of nodes (switches or routers), E = {ei|i = 1, 2, …, n} represents the set of edges (physical lines such as fiber optics or coaxial cables), W = {Wi|i = 1, 2, …, n} with the maximal capacity Wi of ei, C = {ci|i = 1, 2, …, n} with per unit maintenance cost ci of ei, and L = {li|i = 1, 2, …, n} with the lead time li of e
The algorithm to generate (d,B,T)-MPs
Suppose that all Pm are given. All (d,B,T)-MPs can be generated with the following steps.
- Step 0.
[Initialization] Set Θmin,B = Ø, Θmin,T = Ø, and j = 0.
- Step 1.
Find the largest assigned demand such that .
- Step 2.
[Generation of feasible demand set d] Generate all non-negative integer solutions of where dm⩽, m = 1, 2, …, k.
- Step 3.
[Generation of minimal capacity vectors satisfying d and T] For each demand set d, do the following steps.
- 3.1.
Find the minimal capacity vm of Pm such that dm units of
An illustrative example
To illustrate the solution process, we use a random computer network with 13 edges shown in Fig. 3. In this example, each edge is combined with several Optical Carrier 18 (OC-18) lines and each line provides two possible capacities, 1 giga bits per second (Gbps) and 0 bits per second (bps). Since the lines are provided by different suppliers, the capacity of each edge follows a distinct probability distribution. Table 1 provides the capacity, lead time, and per unit maintenance cost of each
Discussion and summary
In Section 4, the total maintenance cost TC(X1) = 500 exceeds the budget B = 480. However, if we delete the unqualified capacity vector X1 = (5,5,5,3,0,0,3,3,1,0,0,1,1) directly, it means the set D1 is also deleted where D1 = {X|X ⩾ X1}. This deletion action unexpectedly removes some X fulfilling d, T, and B. For instance, X1,4 = (5,5,5,4,0,0,3,3,1,0,0,1,1) and X1,7 = (5,5,5,3,0,0,4,3,1,0,0,1,1) adjusted from X1 are removed if X1 is deleted (see Fig. 4). In fact, both X1,4 and X1,7 satisfy not only the
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