In multi-echelon distribution strategy freight is delivered to customers via intermediate depots. Rather than using direct shipments, this strategy is an increasingly popular one in urban logistics. This is primarily to alleviate the environmental (e.g., energy usage and congestion) and social (e.g., traffic-related air pollution, accidents and noise) consequences of logistics operations. This ...

We develop an approximation model for the state-dependent sojourn time distribution of customers or orders in a multi-stage, multi-server queueing system, when interarrival and service times can take on general distributions. The model can be used to make probabilistic statements about the departure time of a customer or order, given the number and location of customers currently in process or ...

We consider a multi-server non-preemptive queue with high and low priority customers, and a decision maker who decides when waiting customers may enter service. The goal is to minimize the mean waiting time for high-priority customers while keeping the queue stable. We use a linear programming approach to find and evaluate the performance of an asymptotically optimal policy in the setting of ex...

An embedded Markov chain is used to analyze a G/M/1 queuing system with N policy. When the system is empty, the server remains idle (deactivates) and does not start serving the waiting customers in the queue until the number of arrivals reaches N. The service is performed in batches of min(n, N) if there are n customers waiting at the completion of service. Service times of the server depend o...

The MX/G/1 queue with finite waiting room is studied for both the partially rejected model and the totally rejected model. We start by studying the joint distribution of the number of customers at time t and the remaining service time of customer in service. This gives the asymptotic distribution of the number of customers at an arbitrary moment and immediately after a departure. Also the waiti...

We study the workload (unfinished work) and the waiting time of the queueing system with MAP arrivals under D-policy. The D-policy stipulates that the idle server begin to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We first set up the system equations for workload and obtain the steady-state distributions of workloads at a...

We study a first passage time problem for a class of spectrally positive Lévy processes. By considering the special case where the Lévy process is a compound Poisson process with negative drift, we obtain the Laplace-Stieltjes transform of the steady-state waiting time distribution of low-priority customers in a twoclass M/GI/1 queue operating under a dynamic non-preemptive priority discipline....

in this paper we introduced a new priority rule algorithm in human queues. the suggested method is applicable in human lines with different demands (serving times) for different customers. in this method, the waiting time for each customer is related to the volume of demand. a common example of such a system is a bakery line. the usual priority rule algorithm in this kind of queue is first-in-f...

This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discreteMarkovian service process. The server terminates service whenever the system becomes empty, and recommencesservice as soon as the number of waiting customers in the queue is N. We obtain the system-length distributionsat pre-arrival and arbitrary epochs using the supplementary...

We consider a multiserver queueing system with two classes of customers: a type 1 (narrow-band, NB) customer requires a single server, while each type 2 (wide-band, WB) customer requests n of the rn servers (n is not random). Servers allocated to a type 2 customer are seized and released simultaneously. Service times are exponentially distributed with mean l/p, for type i customers (i = 1,2). B...