The generalized Erlang blocking model has been used to analyze multiplexing, message storage, and communication network performance. The author modifies this model to permit blocked requests to retry, with reduced resource requirements and arbitrary mean residency requirements. Because the modification of the generalized Erlang model destroys the product-form structure and greatly increases the size of the state space, and exact solution is out of the question. The present approach modifies a well-known one-dimensional recursion developed for the generalized Erlang model in an intuitively satisfying manner, and results in an approximation scheme that is both efficient and quite accurate. This study arose in the context of high-speed networks in which high bandwidth but non-real-time messages may, upon being blocked, request service with smaller bandwidth and larger residency time, as long as the bandwidth-residency time product is the same as originally requested.>

The model studied in this paper captures the combined effects of finite and infinite source traffic-often used to model interactive and batch traffic, respectively-when they contend for a single server resource. The finite source traffic is modeled by heterogeneous finite sources, the infinite source traffic by a stationary Poisson process, and the single server is assumed to have exponentially distributed service times with distinct service rates for the different customer types. All customers share a common queue and are serviced in FIFO order. A special case of this model where theNfinite sources are identical combines two fundamental and widely used models (the repairman andM/M/1models) in a natural manner. Regardless of the homogeneous or heterogeneous nature of the finite sources, the combined source model is not product form due to the realistic assumption that service rates are distinct for different customer types (batch and interactive traffic typically have different CPU processing requirements). In this paper, we show how to recursively calculate all mean quantities of interest in an approximate but quite accurate manner for the general heterogeneous model. The accuracy of the recursive technique is established in part by contrasting the approximate solution to simulation results for a wide parameter range, and in part by studying the asymptotic behavior of the approximation.

Synchronous and asynchronous I/O access disciplines are compared for use in a transaction-processing system. Synchronous access causes an executing process to be suspended while its I/O is performed, whereas asynchronous access permits a process to continue execution concurrently with the servicing of its I/O requests. While it is intuitively clear that asynchronous access generally yields superior performance due to the greater concurrency allowed between transactions, our results considerably sharpen such intuition by quantifying the margin of improvement. The performances of the two disciplines are studied under a variety of conditions by using simple and standard queuing network models. Of particular interest is a situation where an I/O device is congestion-adaptive in service rate. Simulation models for a realistic implementation are described and the results compared with those of the queuing models. The paper concludes by giving guidelines which determine whether, for a particular system, asynchronous I/O is likely to provide a significantly better processing capacity than synchronous I/O. We also observe that similar performance advantages (due to greater transaction concurrency) can be obtained by a transaction-processing architecture which uses re-entrant procedures and dynamically generates a process and data area for each active transaction.

In recent years, considerable effort has focused on evaluating the blocking experienced by "customers" in contending for a commonly shared "resource." The customers and resource in question have typically been messages and storage space in message storage applications or data streams and bandwidth in data multiplexing applications. The model employed in these studies, a multidimensional generalization of the classical Erlang loss model, has been limited to exponentially distributed storage (or data transmission) times, questions concerning efficient computational schemes have largely been ignored, and the class of resource sharing policies considered has been unnecessarily restricted. The contribution of this paper is threefold. We first show that the state distribution (obtained by previous authors) is valid for the large class of residency time distributions which have rational Laplace transforms. Second, we show that, for the important and commonly implemented policy of complete sharing, a simple one-dimensional recursion can be developed which eliminates all difficulty in computing quantities of interest-regardless of both the size and dimensionality of the underlying model. Third, we show that the state distribution holds for completely arbitrary resource sharing policies.