Geo (λ)/ Geo (μ) +G/2 queues with heterogeneous servers operating under FCFS queue discipline
Geo (λ)/ Geo (μ) +G/2 queues with heterogeneous servers operating under FCFS queue discipline
复制标题
Geo (λ)/ Geo (μ) +G/2 队列，异构服务器在 FCFS 队列规则下运行
DOI：
10.12691/ajams-3-2-2
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Sivasamy Ramasamy
中科院分区：
文献类型：
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作者：
Thaga Keaogile;A. Adewole;Sivasamy Ramasamy
本文讨论了一类Geo/Geo+G/2型离散时间排队系统的稳态分析。当k=1，2，…时，按照几何分布的服务时间s1=k个时隙，服务器-1为所有到达的客户提供服务∞，具有质量函数F1(K)==Pr(S1=k)=μ(1-μ)k-1，具有平均速率0或平均服务速率μ2=1/β。当两个不同的服务器作为并行服务提供者操作时，对于经典的先到先服务(FCFS)队列规则的使用提出了一些反对意见，在本工作中考虑了服务器串联配置中的另一种队列规则；目标是如果在平衡的单通道队列中，服务速率突然增加并超过当前的服务容量，则如Krishnamoorthy(1968)所建议的那样，安装一个新的通道来与第一个通道串联工作。针对不同的服务时间分布，利用嵌入方法，给出了系统稳态顾客数的概率母函数(PGF)的精确分析，最重要的是顾客在系统中的实际等待时间期望。这项工作表明，在某些附加的、简单但现实的假设下，可以得到该排队的所有文具概率和其他重要度量。
This article discusses the steady analysis of a discrete time queue of Geo/Geo+G/2 type. All arriving customers are served either by server-1 according to a geometrically distributed service time S1=k slots for k=1,2, …∞, with mass function f1(k)==Pr(S1=k) = μ(1- μ) k-1 with mean rate 0 or mean service rate μ2=1/β. Sequel to some objections raised on the use of the classical 'First Come First Served (FCFS)' queue discipline when the two heterogeneous servers operate as parallel service providers, an alternative queue discipline in a serial configuration of servers are considered in this work; the objective is that if, in a single-channel queue in equilibrium, the service rate suddenly increases and exceeds the present service capacity, install a new channel to work serially with the first channel as suggested by Krishnamoorthy (1968). Using the embedded method subject to different service time distributions we present an exact analysis for finding the ‘Probability generating Function (PGF)’ of steady state number of customers in the system and most importantly, the actual waiting time expectation of customers in the system. This work shows that one can obtain all stationery probabilities and other vital measures for this queue under certain additional and simple but realistic assumptions.