Queueing Delay

Suppose we have material-handling systems available for each link connecting any two service centers, such that no queueing delays take place during part movement. The only time expended on moving parts is the travel time. Let l/p-ap be the average travel time of a part on the Urik (i,j), i,j... 

Total delay (sum of the service delay and queueing delay)... 

Although the PMF of the service delay is the same for periodic and event-driven safety messages, their queueing delays are different due to different arrival patterns for the two different types of safety messages. 

Fig. 4.5 Average delays of a periodic safety message with n/ = 4 for an RSU when I = 150, T = 0.4L, and t = 0 [2]. a Service delay Wj of a fragment, b Batch queueing delay Wq. c In-batch queueing delay Wq2...

Queue size ° Available space ° Overflow occurrences ° Delay... 

Any servicing difficulties and delays, such as preconditions that must be satisfied before electron tunneling occurs, lead to a queue of electrons on the electrode. In other words, the excess charge qM on the electrode becomes more negative, and thus the potential difference across the interface departs from the equilibrium value. The overpotential, therefore, is determined by the electron queue. 

The average delay in a queue is composed of two components waiting time QW2 and service time S2. The waiting time can be formulated a function of bus utilization ratio, U2 ... 

Unnecessary work and delay encountered in indirect and expense work are meiinly due to queues. Workers need to stand in line at the tool crib, the stockroom, or the fax machine, photocopy machine, or some other equipment. Through the application of queuing theory, analysts may be able to determine the waiting time incurred in such activities as well as determine the optimum number of service facilities to improve service quality. 

While Lj = Lj w.p. < >( )). Here, t, is the extra delay at node i, until the next job (outstanding order) is completed. Following the analysis in Ettl et al. (2000), we can approximate as follows (provided node i is also modeled as an MIGI< queue) ... 

A bottleneck station is a station with sufficiently high server utilization to cause substantial delays. These are also called stations in heavy traffic. In a manufacturing system, such stations are often the ones of greatest interest. They typictilly represent the critical resources tmd may be responsible for most of the work-in-process and wriiting. Despite the complexity of the exact analysis of the G/G/1 queue, in heavy traffic the behavior is somewhat simple. It may be shown that the steady-state expected waiting time satisfies... 

Routers introduce a fixed 0.1 ms delay, which accounts for the processing required on each packet and adds to the queuing delay. The insane simulator requires router output queues to be sized in terms of number of packets (we used 64 packet queues in our experiments). The buffering capacity of real routers is given in terms of byte volume, i.e., the number of packets that can be stored in a buffer depends on their size. We choose to deal with fixed size packets to work around this limitation of the simulator program. 

Results for ratios of delays indicate that proportional loss differentiation (i.e., schedule cancellation) is achieved when the outbound route is overloaded and traffic is dropped. However, it is not met in any of the algorithms when the queue falls to 0. This implies that the algorithms basically manipulate the queue of the flow members and scheduling of the members to meet the relative delay and loss guarantees. With this the REP feedback loops used in the closed-loop algorithm appear to be robust to variations in the offered load, and the results of the REP closed-loop algorithm are found to be better than the one without any shift. 

Much of the initial work on pricing problems with multiple classes of customers has been done in the context of a queueing network, where heterge-neous customers arrive with different sensitivites to delay, and pricing may be determined to match the supply (server ability) with the demand (customer s needs). Although in many of these problems inventory is not an explicit decision, the ability to accept or reject orders arriving to the queue implies a corresponding production decision, so we will provide a brief review of this area. For additional references, see [153] for instance. 

Building on this, Mendelson and Whang [105] extend [104] to include multiple classes of users, the authors derive incentive-compatible pricing controls for an M/M/1 queue with constant delay cost per unit job. As defined by Mendelson and Whang, optimal incentive-compatible means that the arrival rate and execution priorities jointly maximize the expected net value of the system while being determined on a decentralized basis , i.e., individual customers determine their service level and whether to join the queue. 

In [66], Ha initially extends [104] to include a service rate decision by homogeneous customers in a GI/GI/1 queue where FIFO (first-in first-out) scheduling is used. For example, the service rate decision may be applicable when a customer has the ability to choose an amount of preprocessing on a task that would affect the server effort required to complete the task. Ha shows that a pricing scheme with a variable fee and fixed rebate based on delay cost... 

In [67], Ha extends this work to consider multiple customer classes that differ in their demand, delay costs, and service costs. For an M/G/s processor sharing queue, he shows that a single fee dependent on the time in the system can coordinate the system, and for an M/G/1 FIFO server, coordination can be effected through a pricing scheme that is quadratic in time of service. 

Few researchers have studied the impact of product structures on flow times, scheduling and due date management policies [41] [56]. For assembly jobs, delays in the system occur not only due to waiting in queues (due to busy resources), but also due to staging, i.e., waiting for the completion of other parts of the job before assembly. Fry et al. [41] study the impact of the following job parameters on the flow time total processing time (sum of all operation... 

Quality Stock turn, days of stock held Capital tied up in stock Stock shortages late deliveries of input materials leading to disruptions and delays Lead times (input and output) Late delivery to customers Customer queues Obsolescent stock (past used by date, out of fashion, out dated technology) Reject rates... 

Customer-friendly consular and border services, with tfaining of personnel to eliminate the undignified interrogation styles, cut visa queues and delays, and make available application forms by post or from Internet sites ... 

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