Abstract
The article presents a comprehensive analysis of mapping the characteristics of Web services to queueing theory models, specifically the M/M/1 queueing model. The authors aim to establish a theoretical foundation for modeling the performance of Web services and deriving response time formulae. The key points covered in the article are as follows: 1. Analyzing the characteristics of Web services: The article examines the six fundamental characteristics of queueing systems, including arrival patterns, service patterns, queue discipline, system capacity, and the number of servers, and maps them to the Web service environment. 2. Representation using Kendall's notation: The Web service characteristics are represented using Kendall's notation, resulting in the M/M/1/∞/FCFS model, where M denotes exponential distributions for arrival and service patterns, 1 represents a single server, ∞ represents infinite system capacity, and FCFS represents the first-come, first-served queue discipline. 3. Derivation of response time formulae: The article provides a detailed derivation of the response time formulae for the M/M/1 model using stochastic processes, Markov chains, and the birth-death process. The derivation incorporates steady-state conditions and results in a formula that calculates the probability of completing a request within a user-specified response time. 4. Practical applications: The derived response time formula can be used by service providers to determine the probability of completing user requests within specified Service Level Agreements (SLAs). By setting a threshold value (filter value), the service provider can select requests with a higher probability of completion for further processing. Overall, the article contributes to the understanding of Web service performance modeling by establishing a theoretical foundation based on queueing theory. The mapping of Web service characteristics to the M/M/1 model and the derivation of response time formulae provide valuable insights for service providers to analyze and optimize the performance of their Web services while adhering to SLAs
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