U. C. Gupta

On the M/G/1 machine interference model with spares

Abstract In this paper a recursive method is developed to obtain the steady state probability distribution of the number of down machines at arbitrary time epoch of a machine interference problem with spares. Various system performance measures, such as average number of down machines, average waiting time for repair, average number of spare machines, average number of operating machines, machine availability and opdrator utilization, etc., have been obtained for a variety of repain time distributions.

Modelling and analysis of M/G^{a,b}/1/N queue – A simple alternative approach

In this paper, we consider a single-server finite-capacity queue with general bulk service rule where customers arrive according to a Poisson process and service times of the batches are arbitrarily distributed. The queue is analyzed using both the supplementary variable and imbedded Markov chain techniques. The relations between state probabilities at departure and arbitrary epochs have been presented in explicit forms.

A new approach to fatigue strength distribution for fatigue reliability evaluation

Abstract This paper deals mainly with the derivation of the fatigue strength distribution as a function of number of cycles to failure. This distribution is derived from the S - N curve representing fatigue. The S - N curve is obtained from the number of cycles to failure at two stress levels, and these number of cycles to failure are in turn assumed to follow a log-normal distribution. For checking the viability of this distribution for the calculation of reliability, the stress distribution taken is a complex distribution, which has been derived elsewhere for the stationary random loading process. For the calculation of reliability, the stress-strength interference technique is used. As the distributions of stress and strength obtained are generally of a complex nature, the stress-strength interference technique cannot be used to have analytical solutions. For this purpose, a recent technique developed to calculate reliability under arbitrary distributions has been used.

Analysis of the MAP/G a , b /1/N Queue

The Markovian arrival process (MAP) is used to represent the bursty and correlated traffic arising in modern telecommunication network. In this paper, we consider a single server finite capacity queue with general bulk service rule in which arrivals are governed by MAP and service times are arbitrarily distributed. The distributions of the number of customers in the queue at arbitrary, post-departure and pre-arrival epochs have been obtained using the supplementary variable and the embedded Markov chain techniques. Computational procedure has been given when the service time distribution is of phase type.

Analysis of finite-buffer multi-server queues with group arrivals: GI X /M/c/N

In this paper, we analyse a multi-server queue with bulk arrivals and finite-buffer space. The interarrival and service times are arbitrarily and exponentially distributed, respectively. The model is discussed with partial and total batch rejections and the distributions of the numbers of customers in the system at prearrival and arbitrary epochs are obtained. In addition, blocking probabilities and waiting time analyses of the first, an arbitrary and the last customer of a batch are discussed. Finally, some numerical results are presented.

A recursive method to compute the steady state probabilities of the machine interference model: (M/G/1)/ K

Abstract In this paper a recursive method is developed to obtain the steady state probability distribution of the number of down machines at arbitrary time epochs of a machine interference model (finite source queue) with arbitrary repair (service) time distribution. The only input required for efficient evaluation of state probabilities is the Laplace-Stieltjes transform (LST) of the repair time distribution. Numerical results for various system performance measures have been presented in the form of tables and graphs for repair time distributions: exponential (M), h-stage Erlang (E h ), deterministic (D), hyperexponential (HE 2 ), h-stage generalized Erlang (GE h ) and uniform U( a , b ). The method is explained analytically by means of a simple example.

Analytic and numerical aspects of batch service queues with single vacation

This paper deals with an M/G/1 batch service queue where customers are served in batches of maximum size b with a minimum threshold value a. The server takes a single vacation when he finds less than a customers after the service completion. The vacation time of the server is arbitrarily distributed. Using the supplementary variable method we obtain the probability generating functions of the queue length distributions at various epochs. We also obtain relations among queue length distributions at arbitrary, service (vacation) termination epochs. Further their evaluation is also discussed. Finally, some numerical results and graphs are presented.

On the finite-buffer bulk-service queue with general independent arrivals: GI/M[b]/1/N

We consider a single server finite-buffer bulk-service queue in which the interarrival and service times are arbitrarily and exponentially distributed, respectively. The service is performed in batches of maximum size b. The distributions of number of customers in the queue at pre-arrival and arbitrary epochs have been obtained. In addition, analysis of waiting time in the queue is also carried out.

Complete analysis of finite and infinite buffer GI/MSP/ 1 queue-A computational approach

We consider a finite buffer single server queue with renewal input and Markovian service process. System length distribution at pre-arrival and arbitrary epochs have been obtained along with some important performance measures. The corresponding infinite buffer queue has also been analyzed.

Computing queue length distributions in MAP/G/1/N queue under single and multiple vacation

This paper studies a single server queue with finite waiting room in which the server takes vacation(s) whenever the system becomes empty and we consider both single and multiple vacation(s). Whereas the input process is a Markovian Arrival Process (MAP), the service and vacation times are arbitrarily distributed. The distributions of number of customers in the queue at service completion, vacation termination, departure, arbitrary and pre-arrival epochs have been obtained. Computational procedure has been given when the service- and vacation-time distributions are of phase type (PH-distribution).