An M/G/1 queue with server vacations and nongated time-limited service is analyzed. A functional equation which characterizes the system behavior is derived. The equation is solved by a numerical technique that approximates the unknown function by a weighted sum of Laguerre functions with unknown coefficients. The functional equation is transformed into a set of linear equations from which the coefficients can be computed. By the work-decomposition and Poisson arrivals see time averages (PASTA) properties, the average customer response time can be readily obtained for the case of exponential service time. Numerical examples are included to demonstrate the validity of the technique.
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机译：分析了具有服务器休假和非门限时服务的M / G / 1队列。得出表征系统行为的函数方程。该方程通过数值技术求解，该技术通过具有未知系数的Laguerre函数的加权和来近似未知函数。将功能方程式转换为一组线性方程式，可以从这些线性方程式计算系数。通过工作分解和泊松到达时间平均（PASTA）属性，对于指数服务时间，可以轻松获得平均客户响应时间。包括一些数字示例，以证明该技术的有效性。
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