A heterogeneous M/M/2/L queueing system in which two servers may work at different rates is considered. A class of threshold type scheduling policies, called fixed position policies (FPPs), is introduced. If first-in first-out (FIFO) delivery is required, departures must wait at the receiving node to be put back into proper sequence. Therefore, they incur resequencing delay in addition to whatever previous delays they experienced. A new approach, based on an imbedded Markov chain model for obtaining the resequencing delay characteristics of FPPs is developed. Closed-form expressions for the distribution and the mean of the resequencing delay are derived. For a given threshold value, the choice of the preferred FPP depends on which optimization criterion issued, such as the mean resequencing delay or the expected resequence buffer occupancy. It is shown that the selection rule for the preferred policy depends only on the ratio of the service rates. However, the optimal policy which minimizes the total delay also depends on the threshold. Application examples of these optimization procedures are presented.>

A system of multiple primary queues with finite waiting rooms, where blocked jobs are allowed to overflow onto a common secondary queue, also with finite waiting room, is considered. Poisson arrivals and exponentially distributed service times, possibly different ones, are assumed at each primary service facility. Service facilities consist of a single server or multiple servers. Based on a simple iterative expression for the Laplace-Stieltjes transform of the interoverflow time distribution, the peakedness of the overflow process from primary queues is studied as a function of the number of primary servers and buffers as well as the original primary load. Behaviors and relations are identified for extreme cases (low offered load or large waiting rooms) and illustrated with examples. An approximation consisting of a natural extension of Hayward's formula to finite waiting room systems is proposed to estimate the blocking seen by the overflow traffic offered to the secondary service facility. Numerical examples covering a wide range of systems show that the approximation is good over a wide range of loads for systems with a single primary queue, as well as at high load for systems with multiple primary queues.>

The resequencing problem is considered in a distributed system environment with multiple classes. A system consisting of two parallel heterogeneous M/M/1 queues shared by C different arrival classes is presented and analyzed. Arriving customers are distributed among the two queues according to a probability distribution which depends upon their class. If customers belong to the same class must depart from the server at the same order as they arrived, they incur additional delay called resequencing delay. A recursive solution technique is first introduced to obtain the exact expression for the expected resequencing delay for a single-class case. The result is then extended to the case of a single class with interfering traffic. Some numerical examples are presented to illustrate changes of resequencing delay as a function of distributed loads to servers.>

In service centers with multiple-parallel servers, jobs may complete their service in a different order from the one in which they enter the center. In order to reestablish the original order, resequencing protocols need to be implemented. It is shown that under a threshold-type policy, the resequencing delay depends on the strategy by which customers are selected and dispatched to the servers. Two selection strategies are developed, and the delay characteristics corresponding to the two strategies are studied. Existing methods for finding the sequencing delay are extended to cover the threshold-type policy. Closed-form solutions for the resequencing delay distributions under both selection policies are derived. To characterize the performance of the system under the two policies, two optimization criteria are introduced, namely, the fraction of customers that experience resequencing delay and the mean resequencing delay. These quantities are calculated explicitly, and their comparison reveals that the optimal decision is independent of the load on the system. The selection of the optimal policy under the first criterion depends only on the service rates, whereas for the second criterion the optimal selection depends on the threshold value and the ratio of the service rates.>

Packet switching networks with flow controlled virtual channels are modeled by closed multi-chain queueing networks. The tree convolution algorithm for an exact analysis of such models is discussed. The algorithm is very efficient when routing chains have sparseness and locality properties that are typical of communication network models. The accuracy of an approximate model of equivalent open chains was investigated. An optimal routing criterion for adding a virtual channel (with a window size of one) to an existing network is explored.

An experimental study was conducted using a network simulator to investigate the performance of packet communication networks as a function of: the network resource capacities (channels, buffers), the network load (number of virtual channels, virtual channel loads), protocols (flow control, congestion control, routing), and protocol parameters (virtual channel window size, input buffer limits). Performance characteristics are shown and the design of input buffer limits for network congestion control, virtual channel window size, and nodal buffer capacity addressed. Network design strategies for the control of load fluctuations are proposed and discussed.