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Full-Text Articles in Probability
(R2077) Enhancing Queue Management: Dynamic Server Allocation And Optional Services In Stochastic Modeling, G. Ayyappan, S. Sankeetha
(R2077) Enhancing Queue Management: Dynamic Server Allocation And Optional Services In Stochastic Modeling, G. Ayyappan, S. Sankeetha
Applications and Applied Mathematics: An International Journal (AAM)
Consider a queueing system with a single server, where customer arrivals follow a Markovian arrival process and service times follow a phase-type distribution. The main server has the capability to recruit an additional server when the number of customers in the system exceeds a certain threshold, denoted as L. Both servers provide normal service to customers, and optional service is provided upon request. The main server takes multiple vacations, with the durations following an exponential distribution with rate parameter η, until there is at least one customer in the system. This system can be represented as a Markov chain process, …
(R2120) Flexible Group Service Map/Ph/1 Queueing Model With Working Vacation And Optional Service, G. Ayyappan, S. Kalaiarasi
(R2120) Flexible Group Service Map/Ph/1 Queueing Model With Working Vacation And Optional Service, G. Ayyappan, S. Kalaiarasi
Applications and Applied Mathematics: An International Journal (AAM)
There are many uses of queues, where services are provided in groups; these types of queues are widely studied in the literature. In this paper we examine a particular queueing model wherein the services are provided in groups and the group size may be less than or equal to the size initially fixed. The arrival follows a Markovian arrival process. The service time of each individual customer follows phase type distribution. The maximum of each customer’s individual service time within a group is defined as the group’s service time. At the service completion moment if there are fewer customers than …
(R1975) Map/Ph(1), Ph(2)/2 Queue With Multiple Vacation, Optional Service, Consultations And Interruptions, G. Ayyappan, S. Sankeetha
(R1975) Map/Ph(1), Ph(2)/2 Queue With Multiple Vacation, Optional Service, Consultations And Interruptions, G. Ayyappan, S. Sankeetha
Applications and Applied Mathematics: An International Journal (AAM)
Two types of services are explored in this paper: regular server and main server, both of which provide both regular and optional services. Customers arrive using the Markovian Arrival Process (MAP), and service time is allocated based on phase type. The regular server uses the main server as a resource. Customers’ service at the primary server is disrupted as a result. When the queue size is empty, the main server can take several vacations. This system has been represented as a QBD Process that investigates steady state with the use of matrix analytic techniques, employing finite-dimensional block matrices. Our model’s …
(R2051) Analysis Of Map/Ph1, Ph2/2 Queueing Model With Working Breakdown, Repairs, Optional Service, And Balking, G. Ayyappan, G. Archana
(R2051) Analysis Of Map/Ph1, Ph2/2 Queueing Model With Working Breakdown, Repairs, Optional Service, And Balking, G. Ayyappan, G. Archana
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a classical queueing system with two types of heterogeneous servers has been considered. The Markovian Arrival Process (MAP) is used for the customer arrival, while phase type distribution (PH) is applicable for the offering of service to customers as well as the repair time of servers. Optional service are provided by the servers to the unsatisfied customers. The server-2 may get breakdown during the busy period of any type of service. Though the server- 2 got breakdown, server-2 has a capacity to provide the service at a slower rate to the current customer who is receiving service …