We consider the M/M/1 queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate… (More)
We consider the processor sharing M/M/1-PS queue which also models balking. A customer that arrives and sees n others in the system " balks " (i.e., decides not to enter) with probability 1 − b n. If b n is inversely proportional to n + 1, we obtain explicit expressions for a tagged customer's sojourn time distribution. We consider both the conditional… (More)
We consider the M/G/1 queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, as well as the unconditional distribution , in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less… (More)
miR-148b has been found to be aberrantly expressed in various tumor types. It has recently been reported to be involved in regulating radioresistance in non-small cell lung cancer (NSCLC) cells. However, its expression level and association with radiosensitivity in human patient samples have not been investigated. Real-time PCR was used to evaluate the… (More)
We consider a processor shared M/M/1 queue that can accommodate at most a finite number K of customers. We give an exact expression for the sojourn time distribution in the finite capacity model, in terms of a Laplace transform. We then give the tail behavior, for the limit K → ∞, by locating the dominant singularity of the Laplace transform.