Tayfur Altiok

Approximate analysis of open networks of queues with blocking: Tandem configurations

An approximation procedure is developed for the analysis of tandem configurations consisting of single server finite queues linked in series. External arrivals occur at the first queue which may be either finite or infinite. Departures from the queuing network may only occur from the last queue. All service times and interarrival times are assumed to be exponentially distributed. The approximation algorithm gives results in the form of the marginal probability distribution of the number of units in each queue of the tandem configuration. Other performance measures, such as mean queue-length and throughput, can be readily obtained. The approximation procedure was validated using exact and simulation data. The approximate results seem to have an acceptable error level.

The Allocation of Interstage Buffer Capacities in Production Lines

Abstract A flow-shop-type production line where the stations are subject to breakdown is modeled as a series of queues. The objective is to find the allocation of interstage buffer capacities that maximizes total profit. The stations, which are modeled as single-server queueing systems, have completion-time distributions of two-stage Coxian type. After a standard transformation to a phase-type state representation, the new system gives rise to a Markov chain. The balance equations for this chain are solved by successive approximations to find the steady-state probability distribution of the number of items at each station, once the buffer capacities are given. A search procedure has been employed to find the optimal buffer capacities.

On the Phase-Type Approximations of General Distributions

Abstract In this paper the approximation of general distributions, with known squared coefficient of variation, by phase-type distributions using the first three moments is studied. The phase-type distributions presented in this paper can be fitted to observed data sets and also can be used to approximate general distributions to be used in analytical models as well as in simulation. Formulas for the approximating distributions are presented and examples are given to show the approximations.

Approximate Analysis of Queues in Series with Phase-Type Service Times and Blocking

Queues in series with phase-type service times and finite queue capacities are considered. Servers may get blocked due to the limited space in queues. An approximation method is developed to compute the steady state probability distributions of the number of units in each queue. Three cases are considered: the first queue has an infinite capacity; the first queue has a finite capacity; and the first server is always busy. The method decomposes the system of tandem queues into individual queues with revised arrival and service processes and with queue capacities. Then, each queue is analyzed in isolation within an iterative scheme which relates these queues to each other. The approximation method is computationally efficient and it appears to have an acceptable error level.

Buffer capacity allocation for a desired throughput in production lines

In this study, we are concerned with finding the minimum-total-buffer allocation for a desired throughput in production lines with phase-type processing times. We have implemented a dynamic programming algorithm that uses a decomposition method to approximate the system throughput at every stage. We provide numerical examples to show the buffer allocation and compare the corresponding simulated throughput and its bounds with the desired throughput.

Risk Analysis of the Vessel Traffic in the Strait of Istanbul

The Strait of Istanbul, the narrow waterway separating Europe from Asia, holds a strategic importance in maritime transportation as it links the Black Sea to the Mediterranean. It is considered as one of the worlds most congested and difficult-to-navigate waterways. Over 55,000 transit vessels pass through the Strait annually, roughly 20% of which carry dangerous cargo. In this study, we have analyzed safety risks pertaining to transit vessel maritime traffic in the Strait of Istanbul and proposed ways to mitigate them. Safety risk analysis was performed by incorporating a probabilistic accident risk model into the simulation model. A mathematical risk model was developed based on probabilistic arguments regarding instigators, situations, accidents, consequences, and historical data, as well as subject-matter expert opinions. Scenario analysis was carried out to study the behavior of the accident risks, with respect to changes in the surrounding geographical, meteorological, and traffic conditions. Our numerical investigations suggested some significant policy indications. Local traffic density and pilotage turned out to be two main factors affecting the risks at the Strait of Istanbul. Results further indicate that scheduling changes to allow more vessels into the Strait will increase risks to extreme levels. Conversely, scheduling policy changes that are opted to reduce risks may cause major increases in average vessel waiting times. This in turn signifies that the current operations at the Strait of Istanbul have reached a critical level beyond which both risks and vessel delays are unacceptable.

Open Networks of Queues with Blocking: Split and Merge Configurations:

Abstract Split and merge configurations of open networks of queues with blocking are analyzed approximately. The approximation procedure developed decomposes these queue networks into individual queues with revised queue capacity and revised arrival and service processes. These individual queues are then analyzed in isolation. The results obtained seem to have an acceptable error level. Stability conditions for these two configurations are also obtained.

Multi-stage, pull-type production/inventory systems

A production/inventory system consisting of multiple stages in series with arbitrary processing times and with intermediate buffer inventories is considered. There is a finished product warehouse at which demand occurs for the finished products according to a compound Poisson process. Inventory levels of both intermediate and finished stocks are controlled by a continuous-review (R, r) inventory control policy. Production at a stage continues until the inventory level in the downstream buffer reaches its target value R. Once the inventory level drops to its reorder level r, the stage undergoes a set-up and production resumes. An approximation method is developed to obtain the steady-state performance measures of the system. Numerical examples are presented to show the accuracy of the proposed method.

Approximate analysis of arbitrary configurations of open queueing networks with blocking

An algorithm for analyzing approximately open exponential queueing networks with blocking is presented. The algorithm decomposes a queueing network with blocking into individual queues with revised capacity, and revised arrival and service processes. These individual queues are then analyzed in isolation. Numerical experience with this algorithm is reported for three-node and four-node queueing networks. The approximate results obtained were compared against exact numerical data, and they seem to have an acceptable error level.

(R, r) production/inventory systems

An ( R , r ) continuous review inventory policy is considered in a production/inventory environment consisting of a production facility and a finished product warehouse for one type of product. The inventory policy indicates that production starts when the stock on-hand reaches r and continues until the stock level reaches R . The demand process is assumed to be compound Poisson and processing times are phase-type. The problem of finding cost minimizing values of r and R is studied through the analysis of the inventory process for both backordering and lost sales cases. Numerical examples are given to show the computational efficiency of the approach and to show the behavior of the optimal R and r with respect to the cost parameters.