This work focuses over the performability analysis of a multi-server retrial queueing model with phase-type inter-retrial times in cellular networks. It is considered that the pattern of the new call arrival and handoff call arrival follows Markovian arrival process (MAP). The service times of both types of calls are phase-type (PH ) distributed with different service rates, and inter-failure & inter-repair times of channels are exponentially distributed. For the prioritization of handoff calls, G channels are kept in reserve for handoff calls. When all the available channels, say S, are busy at the arrival epoch of a handoff call, the handoff call will be dropped. Whereas a new call will be blocked and will have an option to join the orbit of infinite capacity or leave the system without getting the connection, if at least S-G channels are busy. A new call in the orbit, termed as retrial call, retries to get the connection after a random interval which follows PH distribution. This model is analyzed as a level-dependent-quasi-birth-death (LDQBD) process by applying matrix-analytic method (MAM). Further, the closed-form expressions for essential performance measures of the proposed model are derived. Through numerical illustrations, the behaviour of performance measures depending on the various relevant intensities is discussed. An expected cost optimization problem is formulated to determine the optimal value of service intensity and the optimal value of repair intensity. The cost function analysis is executed by employing Simulated Annealing (SA) method.
翻译:这项工作侧重于对蜂窝网络中具有阶段类型跨审时间的多服务器重新排队模式的可执行性分析; 认为新的呼叫抵达和交接呼叫到达的格局是Markovian抵达过程(MAP) 。 两种类型的呼叫的服务时间是阶段类型(PH),分布不同的服务费率,频道的故障和间歇时间是指数性分布的。 为了确定交接时间的优先次序,G频道被保留在交接时间的备用状态中。 当所有可用的频道,例如S,在手动呼叫到达的时段繁忙时,手动呼叫将被放弃。 新的呼叫将被阻断, 并且可以选择加入无限能力轨道, 或者离开系统而不连接, 如果至少S-G频道繁忙的话。 轨道上的新呼叫被称为重审电话, 在PH分发后的随机间隔后重新获得连接。 这个模型被分析为一个水平依赖的分娩(LDQBD) 执行时间段, 手动呼叫将被放弃。 新的呼叫将会被屏住, 新的呼叫会被屏住, 将选择加入无限能力轨道轨道, 或者离开这个系统, 系统, 即使系统, 即使系统, 连接系统, 连接系统连接系统, 连接系统,,,, 运行 最精确的计算 最精确的计算方法是精确的计算 最佳的计算方法。