Overflow Systems Research Articles

Removal of particles using coagulation and flocculation in a dynamic separator

Dynamic separation technology, based on a swirling motion to remove settleable particles, has been used in North America and Europe for treatment of combined storm water and sewer overflow systems. However, treatment is limited to the removal of large settleable particles. In wastewater, a substantial portion of the pollutants can be either in the form of a colloidal suspension or in solution. Investigations were carried out to observe the removal of colloidal particles and dissolved pollutants using a coagulation process in conjunction with a dynamic separator. The effects of flowrate and coagulant dose on the floc size and their subsequent removal efficiency in the separator was studied. The combined process had an efficiency of 95–99% (mass percentage) in the removal of suspended solids, for a range of flowrates between 8 to 10 l/min. Lower efficiencies were observed for flowrates lower than 8 l/min and higher than 10 l/min. The particle size distribution of the overflow and inlet flow of the separator was monitored to investigate the effects of flowrate on the particle size classification in the separator.

A proof of simple insensitive bounds for a pure overflow system

In [1], [4] and [6] simple and intuitively obvious bounds were suggested for various overflow systems and claimed to be insensitive, that is to be valid also in the non-exponential case. This insensitivity was formalized in [4] and [6] when the service distributions have a monotone failure rate. This technical note provides another proof which for the case of a pure overflow system with one customer class extends the insensitivity to the general case.

A proof of simple insensitive bounds for a pure overflow system

In [1], [4] and [6] simple and intuitively obvious bounds were suggested for various overflow systems and claimed to be insensitive, that is to be valid also in the non-exponential case. This insensitivity was formalized in [4] and [6] when the service distributions have a monotone failure rate. This technical note provides another proof which for the case of a pure overflow system with one customer class extends the insensitivity to the general case.

Analysis on Partial Overflow Queueing Systems with Two Kinds of Calls

In this paper, the traffic model of one kind of the partial overflow system is presented and theoretically analyzed, which has remained unsolved up to today. In the partial overflow systems, the considered overflow traffic stream is a part of the traffic stream overflowing from a common trunks group with multiinput calls. The systems with two kinds of calls are treated. Both of the two input traffic streams are assumed to follow the Poisson process and the holding times of the calls are assumed to be identical and follow an exponential distribution. Under these assumptions, analytical formulas are derived to calculate the individual traffic characteristics for both the loss-loss partial overflow system and the wait-loss partial overflow system. With these results, the accuracy of the well-used equivalent random theory in approximating the traffic model offered with partial overflow stream is investigated. The two-input model is a general one and can be used for analyzing the model with more than two inputs. It is expected that the formulas derived in this paper can be Used to improve the accuracy of ERT method as well as used directly.

Channel Utilization and Blocking Probability in a Cellular Mobile Telephone System with Directed Retry

A directed retry facility, which enables subscribers in a mobile telephone system to look for free radio channels in more than one cell, is investigated with respect to blocking probability and channel utilization. An iterative procedure is devised, by which the dependencies among cells can be illustrated. This procedure makes use of theories developed for overflow systems in classical telephony, and proves to be very accurate for the situations under study. Analytical results are compared with simulations and good agreement is observed. Results show that a substantial improvement, compared with systems without a directed retry facility, can be achieved as far as carried traffic is concerned. The improvement is accomplished at the expense of those subscribers who cannot make use of the directed retry facility due to variations in radio coverage.

Properties of the interrupted poisson approximation

The interrupted Poisson approximation for overflow systems is characterized as a lower bound. This allows its performance to be improved and upper bounds produced for queue and loss overflow systems.

An Approximate Formula for Individual Call Losses in Overflow Systems

A simple approximate formula for estimating individual call losses in overflow systems is derived using the interrupted Poisson process. The formula presents good accuracy in the single-overflow model, and it is also applicable to the multioverflow model. It is expected that the present formula is useful for the optimization of systems under given service criteria.

Performance Modeling for Packet Networks with Satellite Overflow Channels

In a packet network using medium speed terrestrial connectivity, average end-to-end delay can be reduced by using highspeed satellite overflow channels despite their propagation delay. To investigate networks of this type analytically, we derive a new basic queueing model for overflow systems with buffered traffic. The simple, closed-form expressions facilitate analysis. Approximations are developed for multiple primary systems with a single overflow channel; these agree with simulation. Using the overflow model analysis indicated the following. The reduced queueing delay to the high capacity overflow channel more than compensated for propagation delay. Inherent, broadcast transmission capabilities of satellite channels reduced overall network delay. The high capacity overflow channels permit networks to withstand substantial nodal imbalance and overloads.

Overflow Models forDimension®; PBX Feature Packages

We present numerical results for some traffic overflow systems with queuing. Traffic is offered by two independent streams to two groups of trunks, with a finite number of waiting spaces for each, and some overflow capability from the primary group to the secondary group. We consider three different overflow systems, two of which model feature packages offered in Dimension <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">®</sup> PBX. For given offered loads and unit mean holding time, we determine the number of trunks and waiting spaces in the two groups so that the blocking probabilities, and the average delays of queued calls do not exceed prescribed values. We also calculate various other quantities, such as the occupancies of the trunk groups and the probability of overflow from the primary group to the secondary group. Finally, we examine the effect on the blocking probabilities and the average delays of varying the loads offered to a given system.

An Overflow System in Which Queuing Takes Precedence

When calls offered to a primary group of trunks find all of them busy, provisions are often made for these calls to overflow to other groups of trunks. Such traffic overflow systems have been of interest for a long time, but recently overflow systems that allow for some calls to be queued have been of importance. In this paper we analyze a traffic overflow system with queuing, which consists of a primary and a secondary group. The system which we consider here differs from the two systems we investigated earlier, in that no overflow from the primary to the secondary is permitted if there is a waiting space available in the primary queue. As with the earlier investigations, we adopt an analytical approach which considerably reduces the dimensions of the problem, and simplifies the calculation of various steady-state quantities of interest. Our results include expressions for the loss probabilities, the average waiting times in the queues, and the average number of demands in service in each group.

Some Traffic Overflow Problems with a Large Secondary Queue

When calls offered to a primary group of trunks find all of them busy, provisions are often made for these calls to overflow to other groups of trunks. Such traffic overflow systems have been of interest for a long time, but recently overflow systems that allow for some calls to be queued have been of importance. In this paper we analyze a traffic overflow system with queuing. The system consists of two groups, a primary and a secondary. We consider two cases which differ in the treatment of demands waiting in the primary queue. We present an analytical approach which is suitable if the secondary queue is large, or even infinite, and we contrast it with an earlier approach of ours which is more suitable if the secondary queue is not large. The analysis considerably reduces the dimensions of the problem and simplifies the calculation of various steady-state quantities of interest. Our results include expressions for the loss probabilities, the average waiting times in the queues, and the average number of demands in service in each group.

Analysis of Some Overflow Problems with Queuing

When calls offered to a primary group of trunks find all of them busy, provisions are often made for these calls to overflow to other groups of trunks. Such traffic overflow systems have been of interest for a long time, but recently overflow systems that allow for some calls to be queued have been of importance. In this paper we analyze a traffic overflow system with queuing. The system consists of two groups, a primary and a secondary. We consider two cases which differ in the treatment of demands waiting in the primary queue. We adopt a novel analytical approach, which considerably reduces the dimensions of the problem and simplifies the calculation of various steady-state quantities of interest. Our theoretical results include expressions for the loss probabilities, the probability of overflow from the primary to the secondary, and the average waiting times in the queues.

On the Calculation of Overflow Systems with a Finite Number of Sources and Full Availiable Groups

This paper deals with the calculation of loss probabilities in overflow systems with a finite number of sources and full available groups. An exact, explicit solution is derived for overflow systems with only one primary group. Furthermore, an exact method is applied in case of overflow systems with two primary groups. For overflow systems with an arbitrary number of primary groups an approximate method is developed which takes into account the variance of offered overflow traffic. This approximate method yields results which are in good agreement with exact calculations and simulation results.