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首页> 外文期刊>SIAM Journal on Control and Optimization >Control of polling in presence of vacations in heavy traffic with applications to satellite and mobile radio systems
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Control of polling in presence of vacations in heavy traffic with applications to satellite and mobile radio systems

机译：通过在卫星和移动无线电系统中的应用来控制在交通繁忙时休假时的轮询

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Consider a queueing system with many queues, each with its own input stream, but with only one server. The server must allocate its time among the queues to minimize or nearly minimize some cost criterion. The allocation of time among the queues is often called polling and is the subject of a large literature. Usually, it is assumed that the queues are always available, and the server can allocate at will. We consider the case where the queues are not always available due to disruption of the connection between them and the server. Such occurrences are common in wireless communications, where any of the mobile sources might become unavailable to the server from time to time due to obstacles, atmospheric or other effects. The possibility of such vacations complicates the polling problem enormously Due to the complexity of the basic problem we analyze it in the heavy traffic regime where the server has little idle time over the average requirements. It is shown that the suitable scaled total workloads converge to a controlled limit diffusion process with jumps. The jumps are due to the effects of the vacations. The control enters the dynamics only via its value just before a vacation begins; hence it is only via the jump value that the control affects the dynamics. This type of model has not received much attention. The individual queued workloads and job numbers can be recovered (asymptotically) from the limit scaled workload. This state space collapse is critical for the effective numerical and analytical work, since the limit process is one dimensional. It is also shown, under appropriate conditions, that the arrival process during a vacation can be approximated by the scaled fluid process. With a suitable nonlinear discounted cost rate, it is shown that the optimal costs for the physical problems converge to that for the limit problem as the traffic intensity approaches its heavy traffic limit. Explicit solutions are obtained in some simple but important cases, and the cmu-rule is asymptotically optimal if there are no vacations. The stability of the queues is analyzed via a perturbed Liapunov function method, under quite general conditions on the data. Finally, we extend the results to unreliable channels where the data might be received with errors and need to be retransmitted. [References: 32]
机译：考虑一个具有许多队列的排队系统，每个队列都有自己的输入流，但只有一个服务器。服务器必须在队列之间分配时间，以最小化或几乎最小化某些成本标准。队列之间的时间分配通常称为轮询，这是大量文献的主题。通常，假定队列始终可用，并且服务器可以随意分配。我们考虑了由于队列与服务器之间的连接中断而导致队列不总是可用的情况。此类情况在无线通信中很常见，在无线通信中，由于障碍物，大气或其他影响，服务器可能会不时出现任何移动源不可用的情况。这种休假的可能性使轮询问题极大地复杂化。由于基本问题的复杂性，我们在交通繁忙的情况下对其进行分析，在这种情况下，服务器的闲置时间很少超过平均需求。结果表明，合适的扩展总工作量收敛到具有跳跃的受控极限扩散过程。跳跃是由于假期的影响。控件仅在休假开始之前才通过其值输入动态。因此，仅通过跳转值，控件才会影响动态效果。这种类型的模型没有受到太多关注。可以从极限扩展的工作负荷中（渐近地）恢复各个排队的工作负荷和作业编号。由于极限过程是一维的，所以这种状态空间的崩溃对于有效的数值和分析工作至关重要。还表明，在适当的条件下，休假期间的到达过程可以通过标定的流体过程来近似。通过适当的非线性折现成本率，可以看出，随着交通强度接近繁重的交通限制，物理问题的最佳成本与极限问题的最优成本趋于一致。在一些简单但重要的情况下，可以得到显式解，并且如果没有休假，则cmu规则是渐近最优的。在相当普遍的数据条件下，通过扰动的Liapunov函数方法分析队列的稳定性。最后，我们将结果扩展到不可靠的通道，在该通道中可能会错误接收数据并需要重新传输数据。 [参考：32]

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