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Telemedicine is a remote medical practice, which utilizes information and communication technology to provide healthcare and exchange of health information for distance places. Diagnosis and prescription for rural and remote area patients are the main advantages of this system. The major categories of telemedicine are store-and-forward, remote patient monitoring and interactive telemedicine. Interactive telemedicine is a real-time interaction between patients and doctors. This method can be conducted in a nursing home or at the patient's house via a video-conferencing system. Moreover, this is more convenient for patients, than to obtain health care with a caretaker in person. However, Internet-based networks are congested with many users. We considered interactive telemedicine as a queueing system and analyzed it by using the method of supplementary variables. We obtained the performance measures through a probability generating function. The numerical results of the queueing system may be useful to provide service satisfactorily and update the utility function of interactive telemedicine. Keywords: Telemedicine, Interactive telemedicine, Queueing system, Supplementary variable technique

In this queueing model service process is split into two phases called first essential service and second essential service. Here the occurrence of breakdown during first essential service and second essential service are different. When the server got failure during first essential service, service process will be interrupted and sent to repair station immediately. On contrary during second essential service when the server got failure the service will not be interrupted, it performs continuously for current batch by doing some technical precaution arrangements. Server will be repaired after the service completion during renewal period. On service completion, if the queue length is less than 'a' then the server leaves for vacation. During vacation if the queue length reaches the value 'a' then the server breaks the vacation and performs preparatory work to start first essential service. Various performance measures and cost effective model with appropriate numerical solution of the model are presented.

This paper concentrates on single server bulk arrival queue system with batch size dependent service and working vacation. The server provides service in two service modes depending upon the queue length. The server provides single service if the queue length is at least ‘a’. On the other hand the server provides fixed batch service if the queue length is at least ‘k’ (k > a). Batch service is provided with some fixed batch size ‘k’. After completion of service if the queue length is less than ‘a’ then the server leaves for working vacation. During working vacation customers are served with lower service rate than the regular service rate. Service during working vacation also contains two service modes. For the proposed model probability generating function of the queue length at an arbitrary time will be obtained by using supplementary variable technique. Some performance measures will also be presented with suitable numerical illustrations.This paper concentrates on single server bulk arrival queue system with batch size dependent service and working vacation. The server provides service in two service modes depending upon the queue length. The server provides single service if the queue length is at least ‘a’. On the other hand the server provides fixed batch service if the queue length is at least ‘k’ (k > a). Batch service is provided with some fixed batch size ‘k’. After completion of service if the queue length is less than ‘a’ then the server leaves for working vacation. During working vacation customers are served with lower service rate than the regular service rate. Service during working vacation also contains two service modes. For the proposed model probability generating function of the queue length at an arbitrary time will be obtained by using supplementary variable technique. Some performance measures will also be presented with suitable numerical illustrations.

Unreliable vacation retrial queue and multi stages of service delay in repair is studied. After completion of the i th (i=1,2,...k) stage of service, the unit may have the option to choose (i+1)th stage of service with probability θi , or with pi may join into orbit to give feedback or may leave the station with probability qi = 1 – pi – θi , (i = 1,2,...k –1) and qi = 1 – pi , (i = k). After service completion if the orbit has no units, server takes avacation. During repair, the unit waiting in the system to complete the remaining service (delay time) is discussed. We analyzed the system using the method of supplementary variable. Simulation results are given using MATLAB.

In this paper, we have considered an MX / (a,b) / 1 queueing system with server breakdown without interruption, multiple vacations, setup times and N-policy. After a batch of service, if the size of the queue is ξ (< a), then the server immediately takes a vacation. Upon returns from a vacation, if the queue is less than N, then the server takes another vacation. This process continues until the server finds atleast N customers in the queue. After a vacation, if the server finds at least N customers waiting for service, then the server needs a setup time to start the service. After a batch of service, if the amount of waiting customers in the queue is ξ (≥ a) then the server serves a batch of min(ξ,b) customers, where b ≥ a. We derived the probability generating function of queue length at arbitrary time epoch. Further, we obtained some important performance measures.

In this paper, server provides service in two service modes, as single or in bulk according to the queue length. The server provides single service, if the queue length reaches value 'a' and batch service, if the queue length reaches the value 'c' (c > a). After completing the service if the queue length is less than 'a' then the server leaves for vacation. During secondary job (vacation) if the queue length attains the value 'a' then the server breaks the vacation and provides primary service. In the service completion epoch if the server is not reliable then the server has undergone renovation of service station. For the proposed model probability generating function of queue size at an arbitrary time epoch is obtained. Various performance measures are derived with suitable numerical illustration. A cost model is also presented for the proposed model.

In this paper, we have investigated bulk retrial queueing system with Bernoulli vacation schedule and variable server capacity. According to the variable server capacity bulk service rule, the server can serve a minimum of one customer and a maximum of B customers in a batch. After completion of a batch of service, if the orbit is empty, then the server will go for a vacation. After completion of each batch of service, if the orbit is non-empty, then the server either go for a vacation with probability p or resumes its service with probability p. If arriving customers finds the server is busy with service or on vacation, they are grouped and it termed as unsatisfied customers or orbit. Unsatisfied customers will retry its appeal for service after some time. We have presented steady state system equations for the proposed model. Also, we have obtained some important performance measures for this system. Further, we have given numerical justification for this queueing system.