We analyze queueing model with priority scheduling by supplementary variable method. Customers are classified into two types ( type-1 and type-2 ) according to their characteristics. Customers of each type arrive by independent Poisson processes, and all customers regardless of type have same general service time. The service order of each type is determined by the queue length of type-1 buffer...

The performance analysis of peer-to-peer (P2P) networks calls for a new kind of queueing model, in which jobs and service stations arrive randomly. Except in some simple special cases, in general, the queueing model with varying service rate is mathematically intractable. Motivated by the P-K formula for M/G/1 queue, we developed a limiting analysis approach based on the connection between the ...

We consider the maximum queue length and the maximum number of idle servers in the classical Erlang delay model and the generalization allowing customer abandonment—the M/M/n+M queue. We use strong approximations to show, under regularity conditions, that properly scaled versions of the maximum queue length and maximum number of idle servers over subintervals [0, t] in the delay models converge...

We study a single queue joining equilibrium when there is uncertainty in the consumers’ minds about the service rate and value. Without such uncertainty, the joining equilibria are characterized by means of a single threshold queue length above which consumers do not join (Naor, 1969). We show that in the presence of such uncertainty, the equilibrium joining strategy is not fully characterized ...

The simplest (stationary) queueing models with catastrophes have been studied some years ago, see for instance [1–6, 9]. Namely, when the queue is not empty, catastrophes may occur with the respective rates. The effect of each catastrophe is to make the queue instantly empty. Simultaneously, the system becomes ready to accept new customers. Nonstationary Markovian queueing models (birthdeath pr...

We consider the fixed-cycle traffic-light (FCTL) queue, where vehicles arrive at an intersection controlled by a traffic light and form a queue. The traffic light signal alternates between green and red periods, and delayed vehicles are assumed to depart during the green period at equal time intervals. Most of the research done on the FCTL queue assumes that the vehicles arrive at the intersect...

Motivated by telephone call centers, we study large-scale service systems with multiple customer classes and multiple agent pools, each with many agents. To minimize staffing costs subject to service-level constraints, where we delicately balance the service levels (SLs) of the different classes, we propose a family of routing rules called Fixed-Queue-Ratio (FQR) rules. With FQR, a newly availa...

There are n queues, each with a single server. Customers arrive in a Poisson process at rate λn, where 0< λ < 1. Upon arrival each customer selects d ≥ 2 servers uniformly at random, and joins the queue at a least-loaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate...

We consider a single-server priority queue with batch arrivals. We treat the head-of-the-line (HL) or preemptive-resume (PR) priority rule. Assuming that the arrival process of batches is renewal for each priority class and using the point process approach, we express the individual class queue-length distribution in terms of the waiting time and the completion time distributions. Assuming furt...

By presenting tourists with real-time information an increase in efficiency and satisfaction of their day planning can be achieved. At the same time, real-time information services can offer the municipality the opportunity to spread the tourists throughout the city centre. An important factor for success is if we can influence tourist day planning. Therefore we studied how tourists could be pe...