Scholarlink

<p>We study a single-server, infinite-buffer queueing system with bulk arrivals and state-dependent batch service governed by the Modified Bulk-Service Rule. In this model, entities arrive in random-sized batches, and service begins only when at least <i>L</i> entities are present. Unlike the traditional General Bulk-Service Rule, entities arriving during service may join theTa ongoing batch, provided the total does not exceed the maximum batch size <i>K</i>. The model is denoted as the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(M^X/M_{r}^{(L \rightarrow K)}/1\)</EquationSource> </InlineEquation> queue. Using the method of roots, we derive the joint probability generating function of the queue-length and the number of entities in service at an arbitrary epoch. Closed-form expressions for the marginal distributions of the number of entities in the queue, in the system, and with the server are obtained. Several performance measures are computed, and Little’s Law is verified. Numerical results are presented in the form of tables and graphs to illustrate the impact of system parameters and batch-size distributions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Markovian Queue with Bulk Arrivals and State-Dependent Service under a Modified Bulk-Service Rule: A Roots Approach to the \(M^{X}/M^{(L \rightarrow K)}_r/1\) System

  • 期刊论文

  • 发表日期：

    2025年12月18日

查看全文
  • Anjana Kumari,
  • Gagandeep Singh

摘要

We study a single-server, infinite-buffer queueing system with bulk arrivals and state-dependent batch service governed by the Modified Bulk-Service Rule. In this model, entities arrive in random-sized batches, and service begins only when at least L entities are present. Unlike the traditional General Bulk-Service Rule, entities arriving during service may join theTa ongoing batch, provided the total does not exceed the maximum batch size K. The model is denoted as the \(M^X/M_{r}^{(L \rightarrow K)}/1\) queue. Using the method of roots, we derive the joint probability generating function of the queue-length and the number of entities in service at an arbitrary epoch. Closed-form expressions for the marginal distributions of the number of entities in the queue, in the system, and with the server are obtained. Several performance measures are computed, and Little’s Law is verified. Numerical results are presented in the form of tables and graphs to illustrate the impact of system parameters and batch-size distributions.