M/G/c/c 대기행렬 모형을 이용한 대학 도서관 보유 장서 최적화

Queueing models have been used to model library management system for about 40 years. While the analytic solutions of the models provide intuition to understand various performance measures of the library system, it is difficult to employ the queueing models to optimization problems due to its complexities. In this paper, we studies the optimization problems in library management by employing M/G/c/c queueing models. To estimate the probability that arrivals find all books unavailable(loss probability), Erlang loss formula in M/G/c/c queue is used. The mathematical model developed here is to decide number of books to buy to ensure a given service quality. Since Erlang loss formula is a nonlinear function of system loading and number of server, the problem belongs to the domain of nonlinear optimization problem. To find an optimal solution, a dynamic programming of the 0-1 Knapsack problem is employed.